Loading [MathJax]/jax/output/SVG/jax.js
Research article

Forecasting the total electricity production in South Africa: Comparative analysis to improve the predictive modelling accuracy

  • Electricity plays an important role in the South African economy with the industrial sector consuming the highest proportion followed by the residential and mining sector. Besides the fact that electricity is considered as an important energy sources, an adequate supply of electricity remains an important factor that affects the development and economic growth of a country. Therefore, it becomes even more important to forecast the total electricity production in South Africa. It turns out that the comparison of the predictive performance of different forecasting methods is inevitable. Hybrid forecasting approaches, such as artificial neural network (ANN) based seasonal Autoregressive Integrated Moving Average (sARIMA) model, ANN based multiplicative Holt-Winters (HW) model, ANN based additive HW model, an adaptive neuro-fuzzy inference system (ANFIS) based sARIMA model, ANFIS based multiplicative HW model and ANFIS based additive HW model, are employed as some valuable alternatives compared with the conventional univariate time series models, such as sARIMA model and both multiplicative and additive HW models. The aim of this study is not only to provide evidence on the weakness of the univariate time series models, but also to show that hybrid forecasting method has the superior ability over the univariate time series models, with achieving a higher forecasting accuracy. In addition, random walk model is used as benchmark model, allowing for the fair competition. The results show that the hybrid model, ANN based on multiplicative HW model, is the most fitted for the total electricity production in South Africa. This study presents an empirical framework to guide the field of prediction research by providing a more comprehensive empirical investigation of the total electricity production forecasting by using various hybrid models.

    Citation: Emrah Gulay. Forecasting the total electricity production in South Africa: Comparative analysis to improve the predictive modelling accuracy[J]. AIMS Energy, 2019, 7(1): 88-110. doi: 10.3934/energy.2019.1.88

    Related Papers:

    [1] Eliza Bánhegyi, Attila Dénes, János Karsai, László Székely . The effect of the needle exchange program on the spread of some sexually transmitted diseases. Mathematical Biosciences and Engineering, 2019, 16(5): 4506-4525. doi: 10.3934/mbe.2019225
    [2] Stephen A. Gourley, Xiulan Lai, Junping Shi, Wendi Wang, Yanyu Xiao, Xingfu Zou . Role of white-tailed deer in geographic spread of the black-legged tick Ixodes scapularis : Analysis of a spatially nonlocal model. Mathematical Biosciences and Engineering, 2018, 15(4): 1033-1054. doi: 10.3934/mbe.2018046
    [3] Wenhao Chen, Guo Lin, Shuxia Pan . Propagation dynamics in an SIRS model with general incidence functions. Mathematical Biosciences and Engineering, 2023, 20(4): 6751-6775. doi: 10.3934/mbe.2023291
    [4] Maoxing Liu, Yuming Chen . An SIRS model with differential susceptibility and infectivity on uncorrelated networks. Mathematical Biosciences and Engineering, 2015, 12(3): 415-429. doi: 10.3934/mbe.2015.12.415
    [5] Jordy Jose Cevallos-Chavez, Fabio Augustu Milner . The impact of partner selection in the transmission dynamics of sexually transmitted viral infections. Mathematical Biosciences and Engineering, 2025, 22(6): 1399-1427. doi: 10.3934/mbe.2025053
    [6] Daniel Maxin, Fabio Augusto Milner . The effect of nonreproductive groups on persistent sexually transmitted diseases. Mathematical Biosciences and Engineering, 2007, 4(3): 505-522. doi: 10.3934/mbe.2007.4.505
    [7] Andrew Omame, Sarafa A. Iyaniwura, Qing Han, Adeniyi Ebenezer, Nicola L. Bragazzi, Xiaoying Wang, Woldegebriel A. Woldegerima, Jude D. Kong . Dynamics of Mpox in an HIV endemic community: A mathematical modelling approach. Mathematical Biosciences and Engineering, 2025, 22(2): 225-259. doi: 10.3934/mbe.2025010
    [8] Guo Lin, Shuxia Pan, Xiang-Ping Yan . Spreading speeds of epidemic models with nonlocal delays. Mathematical Biosciences and Engineering, 2019, 16(6): 7562-7588. doi: 10.3934/mbe.2019380
    [9] Haiyan Wang, Shiliang Wu . Spatial dynamics for a model of epidermal wound healing. Mathematical Biosciences and Engineering, 2014, 11(5): 1215-1227. doi: 10.3934/mbe.2014.11.1215
    [10] Oscar Patterson-Lomba, Muntaser Safan, Sherry Towers, Jay Taylor . Modeling the role of healthcare access inequalities in epidemic outcomes. Mathematical Biosciences and Engineering, 2016, 13(5): 1011-1041. doi: 10.3934/mbe.2016028
  • Electricity plays an important role in the South African economy with the industrial sector consuming the highest proportion followed by the residential and mining sector. Besides the fact that electricity is considered as an important energy sources, an adequate supply of electricity remains an important factor that affects the development and economic growth of a country. Therefore, it becomes even more important to forecast the total electricity production in South Africa. It turns out that the comparison of the predictive performance of different forecasting methods is inevitable. Hybrid forecasting approaches, such as artificial neural network (ANN) based seasonal Autoregressive Integrated Moving Average (sARIMA) model, ANN based multiplicative Holt-Winters (HW) model, ANN based additive HW model, an adaptive neuro-fuzzy inference system (ANFIS) based sARIMA model, ANFIS based multiplicative HW model and ANFIS based additive HW model, are employed as some valuable alternatives compared with the conventional univariate time series models, such as sARIMA model and both multiplicative and additive HW models. The aim of this study is not only to provide evidence on the weakness of the univariate time series models, but also to show that hybrid forecasting method has the superior ability over the univariate time series models, with achieving a higher forecasting accuracy. In addition, random walk model is used as benchmark model, allowing for the fair competition. The results show that the hybrid model, ANN based on multiplicative HW model, is the most fitted for the total electricity production in South Africa. This study presents an empirical framework to guide the field of prediction research by providing a more comprehensive empirical investigation of the total electricity production forecasting by using various hybrid models.


    We consider a material in a region ΩRn, n3, which may be in either of two phases, e.g., solid and liquid (see Figure 1). Let us denote by

    u(t,x)=θ(t,x)θM,    (t,x)Q=(0,T)×Ω, T>0,
    Figure 1.  A material Ω exists in two phases. The dotted lines indicate possible thickness of the continuous region.

    the reduced temperature distribution, where θ(t,x) represent the temperature of the material and θM is the melting temperature (the temperature at which solid and liquid may coexist in equilibrium, separated by an interface).

    In the following we will describe the framework of our problem. So, let us consider the interface as a continuous region, more vast (in which the liquid can coexist with the solid) and of finite thickness, in which the change of phase occurring continuously.

    The following nonlinear parabolic system

    {Cρtu+2tφ=kΔuinQ, αξtφ=ξΔφ+12ξ(φφ3)+sξu (1.1)

    with the non-homogeneous Cauchy-Neumann boundary conditions

    {kνu+hu=w1(t,x)onΣ=(0,T]×Ω,ξνφ=w2(t,x) (1.2)

    and with the initial conditions

    u(0,x)=u0(x),φ(0,x)=φ0(x)onΩ, (1.3)

    represents the mathematical model called the phase field transition system, introduced by G. Caginalp (see [3] and references therein) to model the transition between the solid and liquid phase in melting/solidification process to a matter occupying a region Ω, while:

    u(t,x) - represents the reduced temperature distribution in Q;

    φ(t,x) - is the phase function (the order parameter) used to distinguish between the states (phases) of material which occupies the region Ω at every time t[0,T];

    Cρ=ρV; ρ - the density, V - the casting speed;

    ,k,α,ξ,h are physical parameters representing, respectively: the latent heat, the thermal conductivity, the relaxation time, the measure of the interface thickness, the heat transfer coefficient;

    sξ=m[S]E2σTE, a bounded and positive quantity, expressed by positive and bounded physical parameters: m=11(2F(s))12ds, F(s)=14(s21)2, [S]E - the entropy difference between phases per volume, σ - the interfacial tension, TE - the equilibrium melting temperature (see Caginalp & Chen [4]);

    w1(t,x)W112p,21pp(Σ), p2, - is a given function: the temperature of the surrounding at Ω for each time t[0,T] (can also be interpreted as boundary control);

    w2(t,x)W112p,21pp(Σ) - is a given function;

    u0,φ0W22pp(Ω), with kνu0+hu0=w1(0,x) and ξνφ0=w2(0,x);

    The model (1.1)–(1.3) represents a refinement of the classical Stefan problem (see [21,23,24]) in two phases by adding a new nonlinear parabolic equation, derived from the Euler-Lagrange equations for the free energy in Landau-Ginzburg field theory. This new mathematical model reflects more accurately the physical phenomenon of solidification, like: superheating, supercooling, etc.

    Different other nonlinearities capable to come out the complexity of the physical phenomena (the effect of surface tension, separating zone of solid and liquid states, etc) have been proposed by several authors (see Cârjă, Miranville & Moroşanu [5], Kenmochi & Niezgódka [8], Miranville & Moroşanu [9], Moroşanu [16], Moroşanu & Motreanu [20], Penrose & Fife [22] and Temam [24]). The general nonlinear term in Moroşanu & Motreanu [20], is (possibly) non-convex and non-monotone and cover a large class of nonlinearities, including the known cases as well as other new relevant situations. Moreover, different types of boundary conditions on Σ can be associated to (1.1) (see Moroşanu [16] for more details).

    In the present section we will investigate the solvability of the first boundary value problems of the form (1.1)–(1.3) in the class W1,2p(Q), p2.

    The main result of this section establishes the dependence of the solution u(t,x), φ(t,x) in the nonlinear parabolic system (1.1)–(1.3) on the terms w1(t,x), w2(t,x) in the right-hand side of (1.2).

    Theorem 2.1 Problem (1.1)(1.3) has a unique solution (u,φ) with uW1,2p(Q) and φW1,2ν(Q), where ν=min{q,μ}, qp2. In addition (u,φ) satisfies

    uW1,2p(Q)+φW1,2ν(Q)C[1+u0W22pp(Ω)+φ032pW22qq(Ω)+w1W112p,21pp(Σ)+w2W112p,21pp(Σ)], (2.1)

    where the constant C depends on |Ω| (the measure of Ω), T, n, p, q and physical parameters, but is independent of u, φ, w1 and w2.

    Moreover, given any number Md>0, if (u1,φ1) and (u2,φ2) are solutions to (1.1)(1.3) for the same initial conditions, corresponding to the data w11,w21, w12,w22 W112p,21pp(Σ), respectively, such that φ1Lν(Q), φ2Lν(Q)Md, then the estimate below holds

    u1u2W1,2p(Q)+φ1φ2W1,2ν(Q)C[w11w21W112p,21pp(Σ)+w12w22W112p,21pp(Σ)], (2.2)

    where the constant C depends on |Ω|, T, Md, n, p, q and physical parameters, but is independent of u1,u2, φ1,φ2, w11, w21, w12 and w22.

    Proof. The basic tools in the analysis of the problem (1.1) (see [16] and references there in) are the Leray-Schauder degree theory, the Lp-theory of linear and quasi-linear parabolic equations, as well as the Lions and Peetre embedding Theorem, which ensures the existence of a continuous embedding W1,2p(Q)Lμ(Q), where the number μ is defined as follows

    μ={if   p>32,anypositivenumber3pif   p=32.

    The proof of Theorem 2.1 was given in Moroşanu [16] noting that there formulation differs from this by certain physical parameters, which implies different values for the constant C in (2.1) and (2.2). Moreover, corresponding to different boundary conditions (including nonlinear and nonhomogeneous boundary conditions), similar results were proved in Cârjă, Miranville & Moroşanu [5] and Miranville & Moroşanu [9].

    Corollary 2.2 Under hypotheses H0 and H2 in [20] the problem (1.1) possesses a unique solution (u,φ)W1,2p(Q)×W1,2p(Q).

    Proof. Let w11=w21=w12=w22=w in the Theorem 2.1. Then (2.2) shows that the conclusion of the corollary is true.

    The aim of this section is to use the fractional steps method in order to approximate the solution of the system (1.1)–(1.3), whose uniqueness is guaranteed by Corollary 2.2. To do that, let us associate to the time-interval [0,T] the equidistant grid of length ε=TM, for any integer M1. Then, the following approximating scheme can be written in order to approximate the solution of the nonlinear boundary value problem (1.1)–(1.3):

    {ρVtuε+2tφεkΔuε=0 in Qεi,kνuε+huε=w1(t,x) on Σεi, (3.1)
    {αξtφεξΔφε=12ξφε+sξuε in Qεi,ξνφε=w2(t,x) on Σεi,φε+(iε)=z(ε,φε(iε)), (3.2)

    where Qεi=[iε,(i+1)ε]×Ω, Σεi=[iε,(i+1)ε]×Ω, i=0,,M1, and z(t,φε(iε)) is the solution of the Cauchy problem

    {z(s)+12ξz(s)3=0    s[0,T],z(0)=φε(iε),    φε(0,x)=φ0(x), (3.3)

    computed at s=ε, for i=0,,M1. Here φε+(iε)=limtiεφε(t) and φε(iε)=limtiεφε(t).

    For later use, we set: W=L2(0,T;H1(Ω))W1,2([0,T];(H1(Ω))).

    Definition 3.1. By weak solution to the problem (1.1)–(1.2) we mean a pair of functions (u,φ)W×W which satisfy (1.1)–(1.2) in the following sense

    Qt(ρVu+2φ)ψdxdt+kQuψdxdt+hΣuψdγdt=Σw1ψdγdt, (3.4)
    Q(αξtφζ+ξφζ12ξ(φφ3)ζsξuζ)dxdt=Σw2ζdγdt, (3.5)

    for all (ψ,ζ)L2(0,T;H1(Ω))×L2(0,T;H1(Ω)), together with the initial conditions (1.3). In (3.4) and (3.5) we have denoted by the symbol Q the duality between L2(0,T;H1(Ω)) and L2(0,T;(H1(Ω))).

    The main result of this section is the following

    Theorem 3.2. Assume that u0,φ0W22pp(Ω) with kνu0+hu0=w1(0,x) and ξνφ0=w2(0,x). Let (uε,φε) be the solution of the approximating scheme (3.1)(3.3). Then, for ε0, we have

    (uε(t),φε(t))(u(t),φ(t))stronglyinL2(Ω) (3.6)

    for any t[0,T], where u,φW1,2([0,T];L2(Ω))L(0,T;H2(Ω)) is the weak solution to the problem (1.1)(1.3).

    Proof.(see [2]) The proof is based on compactness methods. As a matter of fact it turns out from Theorem 3.2 that if u0,φ0L2(Ω), then the weak solution (u(t),φ(t)) of the system (1.1)–(1.3) is a strong solution, i.e., it is absolutely continuous in t on [0,T] and satisfies a.e. the system (1.1)–(1.3). So Theorem 3.2 can be also viewed as a constructive way to prove the existence in (1.1)–(1.3).

    The result in Theorem 3.2 remains true by replacing the boundary condition (1.2) with kνu+hu=w(t)g(x) and ξνφ=0 (see [6,7,10,11,12,13,14,15,16,17,18,19]).

    The Cauchy problem (3.3) has the solution

    z(ε,φε(iε,x))=|φε(iε,x)|ξξ+ε(φε(iε,x))2,    i=0,,M1, (3.7)

    and then the general algorithm to compute the approximate solution by means of fractional steps method consist in the following sequence (i denotes the time level)

    Begin algfrac

      i:=0 uε,0=u0, φε,0=φ0 from the initial conditions (1.3);

      For i:=0 to M1 do

        Compute z(ε,φε(iε,x)) from (3.7);

        φε+:=z(ε,φε(iε,x));

         Compute φε,i+1,uε,i+1 solving the linear system (3.1)-(3.2);

      Endfor;

    End.

    A comparison between the fractional steps method and the standard iterative Newton method can be found in Moroşanu [16].

    The finite element method (fem in short) is a general method for approximating the solution of boundary value problems for partial differential equations. This method derives from the Ritz (or Gelerkin) method (see Axelson & Barker [1]), characteristic for the finite element method being the chose of the finite dimensional space, namely, the span of a set of finite element basis functions.

    The steps in solving a boundary value problem using fem are:

    P0. (D) The direct formulation of the problem;

    P1. (V) A variational (weak) formulation for problem (D);

    P2.     The construction of a finite element mesh (triangulation);

    P3.     The construction of the finite dimensional space of test

        function (called finite element basis functions);

    P4. (Vnn) A discrete analogous of (V);

    P5.     Assembly of the system of linear equations;

    P6.     Solve the system in P5.

    The finite element method is used in the sequel in order to deduce the discrete state equations. A conceptual numerical algorithm of fractional step type is then formulated to approximate the weak solution corresponding to (3.1)–(3.2), that is:

    (ρVuεt+2φεt,ψ)+k(uε,ψ)+hΩuεψdxdy=Ωw1ψdxdy, (4.1)
    ψH1(Ω),a.e. in (iε,(i+1)ε),
    αξ(φεt,ζ)+ξ(φε,ζ)12ξ(φε,ζ)=sξ(uε,ζ)+Ωw2ζdxdy, (4.2)
    ζH1(Ω),a.e. in (iε,(i+1)ε),

    together with the initial conditions

    u(0,x)=u0(x),φ(0,x)=φ0(x),xΩ.

    By (,) we have denoted the scalar product in L2(Ω).

    Let ε=T/M be the time step size. We assume that ΩR2 is a polygonal domain. Let Tr be the triangulation (mesh) over Ω and ˉΩ=KTrK, and let Nj=(xk,yl),j=¯1,nn, be the nodes associated to Tr. Denoting by Vnn the corresponding finite element space to Tr, then the basic functions {bj}nnj=1 of Vnn are defined by

    bj(Ni)=δji,i,j=¯1,nn,

    and so

    Vnn=span{b1,b2,...,bnn}.

    For i=¯1,M, we denote by ui and φi the Vnn interpolant of uε and φε, respectively. Then ui,φiVnn and

    ui(x,y)=nnl=1uilbl(x,y)i=¯1,M, (4.3)
    φi(x,y)=nnl=1φilbl(x,y)i=¯1,M, (4.4)

    where uil=uε(ti,Nl), φil=φε(ti,Nl), i=¯1,M, l=¯1,nn are the unknowns to be computed.

    Using in addition an implicit (backward) finite difference scheme in time, we introduce now the discrete equations corresponding to (4.1)–(4.2) as follows (see [7,12,13,14,15,16]) for more explanations)

    {Ruil+2Bφil+εhFRuil=B(ρVui1l+2φi1l+εwi1,l1)SφilsξεBuil=B(αξφi1l+εwi1,l2),    i=¯1,M (4.5)

    where uil and φil, l=¯1,nn, are the vectors of unknowns for time level i.

    From the initial conditions (1.3) we have

    u0(x,y)not=u0(x,y)=nnl=1u0(Nl)bl(x,y),φ0(x,y)not=φ0(x,y)=nnl=1φ0(Nl)bl(x,y), (4.6)

    and then from (4.6) we get (see (4.3)–(4.4))

    u0l=u0(Nl)l=¯1,nn,φ0l=φ0(Nl)l=¯1,nn. (4.7)

    The numerical algorithm to compute the approximate solution by fractional steps method can be obtained from the following sequence (again, i denotes the time level)

    Begin algfrac_fem

      i:=0  Compute u0l,φ0l, l=¯1,nn from (4.7);

      Choose wi,l1=w1(ti,Nl), wi,l2=w2(ti,Nl), NlΩ, i=¯0,M1,l=¯1,nn;

      For i:=1 to M do

        Compute zl=z(,Nl), l=¯1,nn from (3.7);

        φi1:=zl, l=¯1,nn;

       Compute uil, φil, l=¯1,nn, solving the linear system (4.5);

      Endfor;

    End.

    The convergence result established by Theorem 2.1 guaranty that the approximate solution computed by the conceptual algorithm algfrac_fem is in fact the approximate solution of the nonlinear parabolic system (1.1)–(1.3).

    The aim of this section is to present an industrial implementation of conceptual algorithm algfrac_fem established in the preview section (in fact an implementation of the numerical model stated by the linear system (4.5) (see P5)).

    From the thermo-kinetics point of view, the solidification and cooling, as well as the simultaneous heating in a continuous casting process of steel, represents a very complex problem of non-stationary heat and mass transfer (see [25]). To solve at present such a problem it is impossible without numerical models of the temperature field and computer technology. In the sequel we will present in short a continuous casting machine, including the key phenomena of interest and a new numerical model that we have used in the settlement of the problem mentioned above.

    The continuous casting process in the metallurgy. In a modern steel casting machine (its essential features are illustrated in Figure 2), the molten metal is tapped from a ladle into a copper mold (crystallizer). Here, the water-cooled walls of the mold (the primary cooling zone) extract heat what leads to solidify a shell that contains the liquid pool. Below the mold (the secondary cooling zone), the product is supported by rollers and is cooled down by water sprays that extract heat from the surface, and, eventually, the core becomes fully solid when the metallurgical length increase at 12÷13m. After the end of secondary cooling zone the product is cooled only by radiation (traiber). Finally, the continuous-casting product must be cut into the optimum lengths (cutting) to achive a maximum yield of metal.

    Figure 2.  Schematic representation of a continuous casting machine.

    The application of the numerical model (4.5) to the continuous casting process, requires experimental research and measurements of operational parameters at MTC2 from Mittal Steel S.A. Galaţi, as well as laboratory research. So, the most important input data in order to do this are (in round bracket we have written the value used by our Matlab program to do the numerical simulations):

    ● the casting speed (V=12.5 mm/s);

    ● physical parameters:

        the density (ρ=7850 kg/m3),

        the latent heat (=65.28kcal/kg),

        the relaxation time (α=1.0e+2),

        the length of separating zone (ξ=.5),

        the coefficients of heat transfer (h=32.012),

        T=44s;

    ● the boundary conditions: (w1(ti,Nl), NlΩ,  i=¯0,M1,l=¯1,nn, in the primary cooling zone (see Figure 4)), (w1(ti,Nl), NlΩ,  i=¯0,M1,l=¯1,nn, in the secondary cooling zone (see Figure 8)) and w2(ti,Nl)=0, NlΩ,  i=¯0,M1,l=¯1,nn;

    Figure 3.  The triangulation Tr over Ω = [0,650]×[0,220].
    Figure 4.  a) the values wi,l1 on the mobile part b) the values wi,l1 on the immobile part – the primary cooling zone.
    Figure 5.  a) the approximate temperature u1, b) the approximate function φ1.
    Figure 6.  The approximate temperature u5.
    Figure 7.  The approximate temperature u20.
    Figure 8.  The values wi,l1 on the fix part - the secondary cooling zone.

    ● dimensions of cristallizer (650 x 1900 x 220), in mm;

    ● the casting temperature (u0=15300C);

    ● the termal conductivity k(u):

    k(u) = [20 100 200 300 400 500 600 700 800 850 900 1000 1100 1200 1600;

        1.43e-5 1.42e-5 1.42e-5 1.42e-5 1.42e-5 9.5e-6 9.5e-6 9.5e-6 8.3e-6...

        8.3e-6 8.3e-6 7.8e-6 7.8e-6 7.4e-6 7.4e-6].

    Numerical experiments. In Figure 3 it can be seen the number of nodes associated to the mesh Tr in the x1 and x2 – axis directions of one half of a rectangular profile. Considering the symmetrical heat removal from the continuous casting (CC) according to the vertical symmetry axis of the rectangular profile, only a half of the cross-section is used in the computation program.

    The numerical model (4.5) uses the temperatures w(t,x,y),t[0,T], (x,y)Ω measured by the thermocouples; the values are illustrated in the Figure 4.

    Figures 57 represents the approximate solution ui, φi (see (4.3), (4.4)), corresponding to different moments of time (i=1, i=5 and i=M).

    A close examination of the Figures 57 tell us the dimension of the solid and liquid zone resulting by runing the Matlab computation program developed on the basis of the conceptual algorithm algfrac_fem.

    Moreover (see [17]), the shape of the graphs shows the stability and accuracy of the numerical results obtained by implementing the fractional steps method.

    The most interesting aspect that we can observe analysing the Figures 67 are the supercooling and superheating phenomenon.

    ● The solidification model that we have considered in this work consist in a nonlinear system of two parabolic differential equations [4]. This new mathematical description of the real phenomenon reflects more accurately the physical aspects, like: superheating, supercooling (see Figures 7 and 11, for example), the effects of surface tension, separating zone of solid and liquid states, etc.

    Figure 9.  The approximate temperature u20, nkx1=10.
    Figure 10.  The approximate temperature u20, nkx1=20.
    Figure 11.  The approximate temperature u40, nkx1=20.

    ● From numerical point of view, the main difficulty in treating the phase field transition system (1.1) is due to the presence of the nonlinear equation corresponding to phase function φ. Thus it is intensely motivated the work in finding more efficient algorithms in order to compute numerically the solution of such system. A scheme of fractional steps type is considered in this sense. This numerical method avoids the iterative process required by the classical methods (e.g., Newton's type approaches) in passing from a time level to another. Numerical tests show that the fractional steps method is faster (CPU-time spent is very small) and the stability and accuracy are higher (see [16,17]) than the Newton's methods.

    ● The distribution of the temperature and the thickness of the solidifying shell, calculated with the numerical model (4.5) obtained following this technique, show that it really is (see Figures 57). New fundamental material properties can also be extracted by analysing the implementation of the numerical model 4.5 (see Figure 7).

    This model is able to simulate the temperature field of a CCM (Continuous Casting Machine) as a whole or any of its parts. In addition, the program elaborated may be used for different slab profiles. The industrial implementation of the numerical model enable us the analysis of the temperature field of the slab when it passes through primary, secondary and traiber zone. The Figures 911 display the calculated isotherms in the secondary cooling zone, while the Figure 12 display the temperature curves on the mobile part, corresponding to the final time level tM.

    Figure 12.  The temperature on the mobile part in the secondary zone: M=40, nkx1=20.

    ● In order to refer the continuous casting process, the following boundary conditions was considered: νu+hu=w1(t,x,y), where h is the heat transfer coefficient and the given function w1(t,x,y) represents the temperature of the surrounding at t[0,T] and (x,y)Ω, ΩR2.

    Generally, the numerical method considered here can be used to approximate the solution of a nonlinear parabolic equation (system) containing a general nonlinear part.

    ● The numerical solution of the phase field transition system of solidification, approximated by this numerical scheme, can be considered as an admissible one for the corresponding boundary optimal control problem (see [16]), formulated in order to study the optimization of the continuous casting process. The numerical results presented in Figures 9-11 illustrate the accuracy of the numerical model (the influence of the density of the net: M = 20, nkx1 = 10, nky1 = 10; M = 20, nkx1 = 20, nky1 = 10; M = 40, nkx1 = 20, nky1 = 10). So, it is strongly motivated to investigate in further the numerical stability of this new numerical model taking into account all parameters (steel casting parameters, physical parameters, net parameters, etc.)

    A detailed discussions on the errors produced by the fractional steps method, illustrate the influence of time and space parameters as well as of all physical parameters (see [17]).

    The author declares that there is no conflicts of interest in this paper.



    [1] Makridakis S, Hogarth RM, Gaba A (2010) Why forecasts fail. What to do instead. MIT Sloan Manage Rev 51: 83–90.
    [2] Khashei M, Bijari M (2010) An artificial neural network (p, d, q) model for timeseries forecasting. Expert Syst Appl 37: 479–489. doi: 10.1016/j.eswa.2009.05.044
    [3] Bianchi L, Jarrett J, Hanumara RC (1998) Improving forecasting for telemarketing centers by ARIMA modeling with intervention. Int J Forecast 14: 497–504. doi: 10.1016/S0169-2070(98)00037-5
    [4] De Gooijer JG, Hyndman RJ (2006) 25 years of time series forecasting. Int J Forecast 22: 443–473. doi: 10.1016/j.ijforecast.2006.01.001
    [5] Armstrong JS (2006) Findings from evidence-based forecasting: Methods for reducing forecast error. Int J Forecast 2: 583–598.
    [6] Chen CF, Chang YH, Chang YW (2009) Seasonal ARIMA forecasting of inbound air travel arrivals to Taiwan. Transportmetrica 5: 125–140. doi: 10.1080/18128600802591210
    [7] Gelper S, Fried R, Croux C (2010) Robust forecasting with exponential and Holt-Winters smoothing. J Forecast 29: 285–300.
    [8] Permanasari AE, Rambli DRA, Dominic PDD (2011) Performance of univariate forecasting on seasonal diseases: The case of tuberculosis. Software Tools Algorithm Biol Syst, 171–179.
    [9] Omane-Adjepong M, Oduro FT, Oduro SD (2013)Determining the better approach for short-term forecasting of Ghana's inflation: Seasonal ARIMA vs h. Int J Bus Humanities Technol 3: 69–79.
    [10] Rahman A, Ahmar AS (2017) Forecasting of primary energy consumption data in the United States: A comparison between ARIMA and Holter-Winters models. AIP Conf Proc 1885: 020163. doi: 10.1063/1.5002357
    [11] de Oliveira EM, Oliveira FLC (2018) Forecasting mid-long term electric energy consumption through bagging ARIMA and exponential smoothing methods. Energy 144: 776–788. doi: 10.1016/j.energy.2017.12.049
    [12] González JP, San Roque AM, Pérez EA (2018) Forecasting functional time series with a new Hilbertian ARMAX model: Application to electricity price forecasting. IEEE T Power Syst 33: 545–556. doi: 10.1109/TPWRS.2017.2700287
    [13] Lebotsa ME, Sigauke C, Bere A, et al. (2018) Short-term electricity demand forecasting using partially linear additive quantile regression with an application to the unit commitment problem. Appl Energ 222: 104–118. doi: 10.1016/j.apenergy.2018.03.155
    [14] Darbellay GA, Slama M (2000) Forecasting the short-term demand for electricity: Do neural networks stand a better chance? Int J Forecast 16: 71–83. doi: 10.1016/S0169-2070(99)00045-X
    [15] Chatfield C (1993) Neural networks: Forecasting breakthrough or passing fad? Int J Forecast 9: 1–3. doi: 10.1016/0169-2070(93)90043-M
    [16] Chatfield C (1995) Positive or negative? Int J Forecast 11: 501–502. doi: 10.1016/0169-2070(96)83105-0
    [17] Gorr WL, Nagin D, Szczypula J (1994) Comparative study of artificial neural network and statistical models for predicting student grade point averages. Int J Forecast 10: 17–34. doi: 10.1016/0169-2070(94)90046-9
    [18] Church KB, Curram SP (1996) Forecasting consumers' expenditure: A comparison between econometric and neural network models. Int J Forecast 12: 255–267. doi: 10.1016/0169-2070(95)00631-1
    [19] Callen JL, Kwan CC, Yip PC, et al. (1996) Neural network forecasting of quarterly accounting earnings. Int J Forecast 12: 475–482. doi: 10.1016/S0169-2070(96)00706-6
    [20] Tkacz G (2001) Neural network forecasting of Canadian GDP growth. Int J Forecast 17: 57–69. doi: 10.1016/S0169-2070(00)00063-7
    [21] Conejo AJ, Contreras J, Espinola R, et al. (2005) Forecasting electricity prices for a day-ahead pool-based electric energy market. Int J Forecast 21: 435–462. doi: 10.1016/j.ijforecast.2004.12.005
    [22] Chen T, Li L, Huang X (2005) Predicting the fibre diameter of melt blown nonwovens: Comparison of physical, statistical and artificial neural network models. Model Simul Mater Sc 13: 575. doi: 10.1088/0965-0393/13/4/008
    [23] Jain A, Kumar AM (2007) Hybrid neural network models for hydrologic time series forecasting. Appl Soft Comput 7: 585–592. doi: 10.1016/j.asoc.2006.03.002
    [24] Ding S, Hipel KW, Dang Y (2018) Forecasting China's electricity consumption using a new grey prediction model. Energy 149: 314–328. doi: 10.1016/j.energy.2018.01.169
    [25] Hu YC (2017) Electricity consumption prediction using a neural network based grey forecasting approach. J Oper Res Soc 68: 1259–1264. doi: 10.1057/s41274-016-0150-y
    [26] Tektaş M (2010)Weather forecasting using ANFIS and ARIMA models. Environ Res Eng Manage 51: 5–10.
    [27] Yayar R, Hekim M, Yilmaz V, et al. (2011) A comparison of ANFIS and ARIMA Techniques in the Forecasting of Electric Energy Consumption of Tokat Province in Turkey. J Econ Soc Stud 1: 87. doi: 10.14706/JECOSS11124
    [28] Yadav RK, Balakrishnan M (2014) Comparative evaluation of ARIMA and ANFIS for modeling of wireless network traffic time series. EURASIP J Wirel Commun Network 2014: 15. doi: 10.1186/1687-1499-2014-15
    [29] Hernandez CAS, Pedraza LFM, Salcedo OJP (2010) Comparative analysis of time series techniques ARIMA and ANFIS to forecast wimax traffic. Online J Electron Electric Eng 2: 223–228.
    [30] Lusis P, Khalilpour KR, Andrew L, et al. (2017) Short-term residential load forecasting: Impact of calendar effects and forecast granularity. Appl Energ 205: 654–669. doi: 10.1016/j.apenergy.2017.07.114
    [31] Luo J, Hong T, Fang SC (2018) Benchmarking robustness of load forecasting models under data integrity attacks. Int J Forecast 34: 89–104. doi: 10.1016/j.ijforecast.2017.08.004
    [32] Li C, Tao Y, Ao W, et al. (2018) Improving forecasting accuracy of daily enterprise electricity consumption using a random forest based on ensemble empirical mode decomposition. Energy 165: 1220–1227. doi: 10.1016/j.energy.2018.10.113
    [33] Chen Y, Kloft M, Yang Y, et al. (2018) Mixed kernel based extreme learning machine for electric load forecasting. Neurocomputing 312: 90–106. doi: 10.1016/j.neucom.2018.05.068
    [34] Zhang G, Patuwo BE, Hu MY (1998) Forecasting with artificial neural networks: The state of the art. Int J Forecast 14: 35–62. doi: 10.1016/S0169-2070(97)00044-7
    [35] Khashei M, Bijari M, Ardali GAR (2009) Improvement of auto-regressive integrated moving average models using fuzzy logic and artificial neural networks (ANNs). Neurocomputing 72: 956–967. doi: 10.1016/j.neucom.2008.04.017
    [36] Kunst RM (2012) Econometric forecasting. Institute for Advanced Studies Vienna and University of Vienna, Available from: http://homepage. univie. ac. at/robert. kunst/progpres. pdf.
    [37] Kler AM, Tyurina EA, Mednikov AS (2018) A plant for methanol and electricity production: Technical-economic analysis. Energy 165: 890–899. doi: 10.1016/j.energy.2018.09.179
    [38] World Meteorological Organization (2015) The Climate in Africa in 2013. WMO, No 1147.
    [39] Chellaney B (2013) Water, peace, and war: Confronting the global water crisis. Rowman & Littlefield.
    [40] Sparks D, Madhlopa A, Keen S, et al. (2014) Renewable energy choices and their water requirements in South Africa. J Energ South Afr 25: 80–92.
    [41] Holt CC (2004) Forecasting seasonals and trends by exponentially weighted moving averages. Int J Forecast 20: 5–13. doi: 10.1016/j.ijforecast.2003.09.015
    [42] Winters PR (1960) Forecasting sales by exponentially weighted moving averages. Manage Sci 6: 324–342. doi: 10.1287/mnsc.6.3.324
    [43] Box GE, Jenkins GM (1970) Time series analysis: Forecasting and control. San Francisco: Holden-Day.
    [44] Rumelhart DE, Hinton GE, Williams RJ (1986) Learning representations by back-propagating errors. Nature 323: 533. doi: 10.1038/323533a0
    [45] Jang JS (1993) ANFIS: Adaptive-network-based fuzzy inference system. IEEE T Syst Man Cy 23: 665–685. doi: 10.1109/21.256541
    [46] Makridakis S, Hibon M (1979) Accuracy of forecasting: An empirical investigation. J Roy Stat Soc 142: 97–125. doi: 10.2307/2345077
    [47] Rojas I, Valenzuela O, Rojas F, et al. (2008) Soft-computing techniques and ARMA model for time series prediction. Neurocomputing 71: 519–537. doi: 10.1016/j.neucom.2007.07.018
    [48] Pankratz A (1983) Forecasting with Univariate Box-Jenkins Models: Concepts and Cases. John Wiley and Sons, New York.
    [49] Makridakis S, Wheelwright SC, Hyndman RJ (2008) Forecasting methods and applications. John wiley & sons.
    [50] Kaboudan MA (2001) Compumetric forecasting of crude oil prices. Evolutionary Computation, 2001, Proceedings of the 2001 Congress on, IEEE, 1: 283–287. doi: 10.1109/CEC.2001.934402
    [51] Rasouli S, Tabesh H, Etminani K (2016) A Study of Input Variable Selection to Artificial Neural Network for Predicting Hospital Inpatient Flows. Brit J Appl Sci Techonol 18: 1–8.
    [52] Kecman V (2001) Learning and soft computing: support vector machines, neural networks, and fuzzy logic models. MIT press.
    [53] Kurkova V (1992) Kolmogorov's theorem and multilayer neural networks. Neural Networks 5: 501–506. doi: 10.1016/0893-6080(92)90012-8
    [54] Zhang P (2003) Time Series Forecasting using a hybrid ARIMA and neural network model. Neurocomputing 50: 159–175. doi: 10.1016/S0925-2312(01)00702-0
    [55] Diebold FX, Mariano RS (1995) Comparing Predictive Accuracy. J Bus Econ Stat 13: 253–263.
  • This article has been cited by:

    1. Shadi Alkhayyat, Mona Khojah, Masaheer AlJehan, Daniah Allali, Almoutaz Tayeb, Sultan Albukhari, N Qusty, R Al-Wassia, R Baljoon, Awareness of Colorectal Cancer in Saudi Arabia: Cross-Sectional Study, 2021, 12, 2229-5402, 38, 10.51847/f5Z7stoOfT
    2. Nazim Faisal Hamid, Fayez Muawwadh Albalawi, Abdulrahman Abdullah Aloufi, Rawapy Ali Hamas, Nasser Awadh H Alanazi, Tariq Hulayyil Alanazi, Epidemiological Trends in Childhood Cancer in Saudi Arabia, 2022, 11, 2278-0513, 42, 10.51847/TkpqjgHEDQ
    3. Hussah M. Alobaid, Maha H. Daghestani, Nawal M. AL-Malahi, Sabah A. Alzahrani, Lina M. Hassen, Dina M. Metwally, Exploring the effect of silver nanoparticles on gene expression in colon cancer cell line HCT116, 2022, 11, 2191-9550, 1108, 10.1515/gps-2022-0094
    4. Adnan Alharbi, Cost-effectiveness of Tamoxifen versus Anastrozole in post-menopausal women with breast cancer: Saudi Arabia perspective, 2022, 1658-905X, 8, 10.37881/jmahs.122
    5. Nada E Algethami, Amjad A Althagafi, Rawan A Aloufi, Fawaz A Al Thobaiti , Hamma A Abdelaziz, Invasive Lobular Carcinoma of the Breast With Rectal Metastasis: A Rare Case Report, 2022, 2168-8184, 10.7759/cureus.23666
    6. Basim Saleh Samman, Albadr Hussein, Razan Saleh Samman, Abdulaziz Saud Alharbi, Common Sensitive Diagnostic and Prognostic Markers in Hepatocellular Carcinoma and Their Clinical Significance: A Review, 2022, 2168-8184, 10.7759/cureus.23952
    7. Laila Naif Al-Harbi, Ghedier M. Al-Shammari, Pandurangan Subash-Babu, Mohammed A. Mohammed, Roaa Ahmed Alkreadees, Abu ElGasim Ahmed Yagoub, Cinchona officinalis Phytochemicals-Loaded Iron Oxide Nanoparticles Induce Cytotoxicity and Stimulate Apoptosis in MCF-7 Human Breast Cancer Cells, 2022, 12, 2079-4991, 3393, 10.3390/nano12193393
    8. Mohammed Alessa, Maryam O Alarfaj, Hanan A Albenayyan, Almaha A Aleidan, Fatimah A Albahrani, May A Bokhuwah, Raghad M Bukhamsin, Razan M Alzahrani, Mohammed F Alkhalifah, Lamees A Alshekhmobarak, Hajar K Alsaleem, Renad S AlSubaie, Dalal A Almulhim, Aisha A AlJughaiman, Lama A Alobaid, Awareness of the Link Between the Consumption of Ultra-Processed Food and Colorectal Cancer Risk in Saudi Arabia, 2023, 2168-8184, 10.7759/cureus.33774
    9. Consuela Cheriece Yousef, Mansoor Ahmed Khan, Hind Almodaimegh, Majed Alshamrani, Meteb O. Alfoheidy, Hana AlAbdalkarim, Ahmed AlJedai, Anjum Naeem, Ivo Abraham, Cost-efficiency analysis of conversion to biosimilar filgrastim for supportive cancer care and resultant expanded access analysis to supportive care and early-stage HER2+ breast cancer treatment in Saudi Arabia: Simulation study, 2023, 1369-6998, 1, 10.1080/13696998.2023.2183680
    10. Ali G Alghamdi, Zahraa Jumah A Almuhanna, Zainab Hussain M Bu Hulayqah, Fatimah Abdulaziz G Algharsan , Hashim A Alghamdi, Hadeel A Alzahrani , Public Awareness of Colorectal Cancer Screening in the Al-Baha Region, Saudi Arabia, 2022, 2022, 2168-8184, 10.7759/cureus.32386
    11. Anfal Mohammed Alenezi, Ashokkumar Thirunavukkarasu, Farooq Ahmed Wani, Hadil Alenezi, Muhannad Faleh Alanazi, Abdulaziz Saud Alruwaili, Rasha Harbi Alashjaee, Faisal Harbi Alashjaee, Abdulaziz Khalid Alrasheed, Bandar Dhaher Alshrari, Female Healthcare Workers’ Knowledge, Attitude towards Breast Cancer, and Perceived Barriers towards Mammogram Screening: A Multicenter Study in North Saudi Arabia, 2022, 29, 1718-7729, 4300, 10.3390/curroncol29060344
    12. Jumanah T Qedair, Abdullah A Al Qurashi, Turki Alfayea, Hatan Mortada, Ali Alsudais, Saleh Almuntashiri, Alqassem Y Hakami, Level and predictors of breast cancer awareness among Saudi women: A nationwide study, 2022, 18, 1745-5057, 174550572211338, 10.1177/17455057221133835
    13. Abdulrahman S. Bazaid, Ahmed A. Punjabi, Abdu Aldarhami, Husam Qanash, Ghaida Alsaif, Hattan Gattan, Heba Barnawi, Bandar Alharbi, Abdulaziz Alrashidi, Abdulaziz Alqadi, Bacterial Infections among Patients with Chronic Diseases at a Tertiary Care Hospital in Saudi Arabia, 2022, 10, 2076-2607, 1907, 10.3390/microorganisms10101907
    14. Hussain Alyousif, Ishag Adam, Naser A. Alamin, Mona A. Sid Ahmed, Ayat Al Saeed, Abdulmuhsen Hussein Hassoni, Imad R. Musa, The prevalence and associated predictors for Bethesda III–VI for reporting thyroid cytopathology in Royal Commission Hospital, Kingdom of Saudi Arabia, 2022, 13, 2042-0188, 204201882211224, 10.1177/20420188221122486
    15. Ahmed M. Basudan, Breast Cancer Incidence Patterns in the Saudi Female Population: A 17-Year Retrospective Analysis, 2022, 58, 1648-9144, 1617, 10.3390/medicina58111617
    16. Mohammed A. AlJaffar, Sari S. Enani, Ahmad H. Almadani, Fay H. Albuqami, Khalid A. Alsaleh, Fahad D. Alosaimi, Determinants of quality of life of cancer patients at a tertiary care medical city in Riyadh, Saudi Arabia, 2023, 14, 1664-0640, 10.3389/fpsyt.2023.1098176
    17. Mohamed Ahmed Bealy, Awad Aljeed Abugooda, Ruba Mustafa Elsaid Ahmed, Nuha Abdel Rahman Khalil, Abdelbaset Mohamed Elasbali, Ghorashy Eltayeb Yousif Mohamed, Faris Merghani Eltom, Hussain Ahmed, Stephane Zingue, Patterns of Immunohistochemical Expression of P53, BCL2, PTEN, and HER2/neu Tumor Markers in Specific Breast Cancer Lesions, 2022, 2022, 1741-4288, 1, 10.1155/2022/2026284
    18. Hasan Ahmed H Baz, Saeed H. Halawani, Ibrahim Abdulaziz, Majid Ali, Nhal Ahmed Baz, Mohammed Jafal, Khaldoun Saleh, Regorafenib Adverse Drug Reactions among Patients in King Abdullah Medical City; A Chart Review Study, 2022, 11, 2277-3657, 24, 10.51847/IexPv4xRns
    19. Ahmad Almatroudi, Brain Tumors in Saudi Arabia: An Observational and Descriptive Epidemiological Analysis, 2022, 10, 2227-9032, 1796, 10.3390/healthcare10091796
    20. Firas S. Azzeh, Deena M. Hasanain, Alaa H. Qadhi, Khloud J. Ghafouri, Wedad F. Azhar, Mazen M. Ghaith, Abdullah F. Aldairi, Hussain A. Almasmoum, Hamza M. Assaggaf, Maha H. Alhussain, Ahmad A. Alghamdi, Mahmoud M. Habibullah, Waleed M. Bawazir, Sofyan S. Maghaydah, Maysoun S. Qutob, Awfa Y. Alazzeh, Consumption of Food Components of the Mediterranean Diet Decreases the Risk of Breast Cancer in the Makkah Region, Saudi Arabia: A Case-Control Study, 2022, 9, 2296-861X, 10.3389/fnut.2022.863029
    21. Sawsan Abdullah Alshahrani, Wedad Saeed Al-Qahtani, Nawaf Abdulrahman Almufareh, Dalia Mostafa Domiaty, Gadah Ibraheem Albasher, Fatmah Ahmed Safhi, Fatima Abdullah AlQassim, Mashael Alhumaidi Alotaibi, Tahani Mohamed Al-Hazani, Bassam Ahmed Almutlaq, Oral cancer among Khat users: finding evidence from DNA analysis of nine cancer-related gene mutations, 2021, 21, 1472-6831, 10.1186/s12903-021-01981-7
    22. Attiah Khobrani , Yasser Alatawi , Eshtyag Bajnaid, Omima Alemam, Abubakr Osman , Lina Bin Attash , Mohammed Jaffal , Mohammed AlGhanmi , Adnan Alharbi, Mohammed Alnuhait, Adherence to Hormonal Therapy in Breast Cancer Patients in Saudi Arabia: A Single-Center Study, 2022, 2168-8184, 10.7759/cureus.24780
    23. Hussain Gadelkarim Ahmed, Amel Bakri Mohammed El Hag, Khulaif Khalaf Alanazi, Hend M. Alkwai, Ahmed Mohmmed Ahmed Abdrhman, Abdelmuhsin Omer Ahmed Hassan, Ibrahim Abdelmageed Mohamed Ginawi, Abdelbaset Mohamed Elasbali, Hisham Sherfi, Histopathologic metrics of breast tumors in Northern Saudi Arabia, 2022, 15, 2689-5293, 649, 10.1080/26895293.2022.2082540
    24. Osamah Ahmad Hakami, Refah Asheer Alsubaie, Bayan Abdulhadi Albaqami, Haifa Matar Almutlaq, Nourah Mushabab Alqahtani, Manal Alkhonezan, Farah Fahad Almuqrin, Abdullah Hussien Alghamdi, Abdullah Abdulaziz Alaryni, Rayan Abubakker Qutob, Knowledge and Perception of Physicians of Different Specialties in Saudi Arabia Toward Helicobacter pylori, 2023, Volume 16, 1178-2390, 763, 10.2147/JMDH.S403999
    25. Majed Ramadan, Rwiah Alsiary, Noor Alsaadoun, Noara Alhusseini, Muhammad Raihan Sajid, Noor Mohamed Hamed, Tarek Ziad Arabi, Belal Nedal Sabbah, Risk of Breast Cancer Progression after Treatment in the Western Region of Saudi Arabia, 2023, 17, 1178-2234, 117822342311582, 10.1177/11782234231158270
    26. Ryanh H Alanazi, Anas Fathuldeen, Malik A Hussain, Ziyad Alharbi, Layan T Almazyad, Hadeel T Alanazi, Khulud Hamed S Alshammari, Shmoukh Mushref Alruwaili, Madhawi A Alanazi, Manal S Fawzy, Breast Cancer Knowledge and Associated Behaviors in Northern Borders, Saudi Arabia: A Cross-Sectional Study, 2024, 2168-8184, 10.7759/cureus.59893
    27. Mohammad H. Aljawadi, Nora Alkhudair, Marwan Alrasheed, Abdulaziz S. Alsuhaibani, Basil J. Alotaibi, Mansour Almuqbil, Abdullah M. Alhammad, Azhar Arafah, Farjah H. AlGahtani, Muneeb U. Rehman, Understanding the Quality of Life Among Patients With Cancer in Saudi Arabia: Insights From a Cross-Sectional Study, 2024, 31, 1073-2748, 10.1177/10732748241263013
    28. Shabihul Fatma Sayed, Hamad G. Dailah, Sumathi Nagarajan, Siddig Ibrahim Abdelwahab, Shaived S. Hasan Abadi, Nida Akhtar, Gulrana Khuwaja, Wadeah Ali DA Malham, Knowledge of Non-Invasive Biomarkers of Breast Cancer, Risk Factors, and BSE Practices Among Nursing Undergraduates in Farasan Island, KSA, 2024, 10, 2377-9608, 10.1177/23779608241248519
    29. Suha A Alhebshi, Safaa M Alsanosi, Hamsa S AlQashqri, Yosra Z Alhindi, Ghazi A Bamagous, Nahla A Ayoub, Alaa H Falemban, Toxicity of Nab-Paclitaxel Compared to Paclitaxel in a Tertiary Hospital in Jeddah, Saudi Arabia: A Retrospective Cohort Study, 2023, 2168-8184, 10.7759/cureus.39872
    30. Ahmed M Alessa, Abdul Sattar Khan, Epidemiology of Colorectal Cancer in Saudi Arabia: A Review, 2024, 2168-8184, 10.7759/cureus.64564
    31. Mohammed Erkhawan Hameed Rasheed, Mansour Youseffi, Luca Parisi, Farideh Javid, Saeed Afshin Javid, 2023, 2872, 0094-243X, 120015, 10.1063/5.0162992
    32. Afnan F Alshehri, Ahmed E Khodier, Mohammed M Al-Gayyar, Antitumor Activity of Ligustilide Against Ehrlich Solid Carcinoma in Rats via Inhibition of Proliferation and Activation of Autophagy, 2023, 2168-8184, 10.7759/cureus.40499
    33. Mohamed A Ghowinam, Ammar A Albokhari, Ahmed M Badheeb, Mohamed Lamlom, Mari Alwadai, Aseel Hamza, Ali Aladalah, Prevalence of Depression and Anxiety Symptoms Among Patients With Cancer in Najran, Saudi Arabia, 2024, 2168-8184, 10.7759/cureus.54349
    34. Turki M Alanzi, Wala Alzahrani, Nouf S Albalawi, Taif Allahyani, Atheer Alghamdi, ‏Haneen Al-Zahrani, ‏Awatif Almutairi, Hayat Alzahrani, Latifah Almulhem, Nouf Alanzi, Abdulrhman Al Moarfeg, ‏Nesren Farhah, Public Awareness of Obesity as a Risk Factor for Cancer in Central Saudi Arabia: Feasibility of ChatGPT as an Educational Intervention, 2023, 2168-8184, 10.7759/cureus.50781
    35. Omalkhair Abulkhair, Ahmad Omair, Dorothy Makanjuola, Manal Al Zaid, Lolwah Al Riyees, Nafisa Abdelhafiez, Emad Masuadi, Ghaida Alamri, Fatinah Althan, Abdulmohsen Alkushi, Ann Partridge, Breast Cancer in Young Women: Is It Different? A Single-Center Retrospective Cohort Study, 2024, 18, 1179-5549, 10.1177/11795549241228235
    36. Ahmed Alasker, Seham Alsalamah, Nada Alshathri, Nura Almansour, Faris Alsalamah, Mohammad Alghafees, Mohammad AlKhamees, Bader Alsaikhan, Performance of large language models (LLMs) in providing prostate cancer information, 2024, 24, 1471-2490, 10.1186/s12894-024-01570-0
    37. Nasser Al Shanbari, Abdulrahman Alharthi , Salah M Bakry, Muath Alzahrani, Majed M Alhijjy, Hashem A Mirza, Meshal Almutairi, Samar N Ekram, Knowledge of Cancer Genetics and the Importance of Genetic Testing: A Public Health Study, 2023, 2168-8184, 10.7759/cureus.43016
    38. Ali G Alghamdi, Alshareef M Alshareef, Aghnar T Alzahrani, Ziyad S Alharthi, Sarah S Alghamdi, Ahmed M Alghamdi, Faisal A Alzahrani, Reem A Alzahrani, Knowledge and Awareness About Gastric Cancer Among the General Population in Al-Baha City, Saudi Arabia, 2023, 2168-8184, 10.7759/cureus.39589
    39. Anwar Ali Jammah, Ibrahim Mohammed AlSadhan, Ebtihal Y. Alyusuf, Mubarak Alajmi, Abdullah Alhamoudi, Mohammed E. Al-Sofiani, The American Thyroid Association risk stratification and long-term outcomes of differentiated thyroid cancer: a 20-year follow-up of patients in Saudi Arabia, 2023, 14, 1664-2392, 10.3389/fendo.2023.1256232
    40. Turki Alelyani, Maha M. Alshammari, Afnan Almuhanna, Onur Asan, Explainable Artificial Intelligence in Quantifying Breast Cancer Factors: Saudi Arabia Context, 2024, 12, 2227-9032, 1025, 10.3390/healthcare12101025
    41. Sahar M Alnefaie, Mohammed A Alosaimi, Meshal F Althobaiti, Abdulmajeed A Altowairqi, Mohammed K Alrawqi, Sami M Alzahrani, Ghaliah O Alnefaie, Maryam S Aljaid, Analyzing Cardiovascular Characteristics of Patients Initially Diagnosed with Breast Cancer in Saudi Arabia, 2023, 2168-8184, 10.7759/cureus.45799
    42. Hamad Albagieh, Shaima E Alabdulkareem, Wajd Alharbi, Shahd M Alqahtani, Ghayda Algoblan, Oral Squamous Cell Carcinoma Mimicking Lichenoid Reaction After Implant Placement: A Case Report, 2023, 2168-8184, 10.7759/cureus.50804
    43. Naushad Abid, Abdullah H Bohamad, Hussain I Aljohar, Batla S Al Battat, Yousef Y Altaher, Abdulaziz E Alateeq, Maryam O Alarfaj, Meataz Aljeezan, Ali S AlBashrawi, Ahmed Al Jizan‎, Knowledge and Awareness of Leukemia Among the Population of Eastern Province, Saudi Arabia, 2023, 2168-8184, 10.7759/cureus.46382
    44. Mudassar Shahid, Ahmed L. Alaofi, Mohammed S. Alqahtani, Rabbani Syed, Genetic implications of PSMA expression variability in breast cancer subtypes with a focus on triple-negative breast cancer, 2024, 65, 1234-1983, 505, 10.1007/s13353-023-00814-3
    45. Hadi Afandi Al-Hakami, Jamelah F Altayyeb, Salwan M Alsharif, Mohammad A Alshareef, Baraa I Awad, Mohammed Al-Garni, Preoperative Thyroid-Stimulating Hormone Levels and Risk of Thyroid Cancer in Post-thyroidectomy Patients for Thyroid Nodules: A Study From a Tertiary Hospital in Western Saudi Arabia, 2023, 2168-8184, 10.7759/cureus.47622
    46. Usman Naseem, Junaid Rashid, Liaqat Ali, Jungeun Kim, Qazi Emad Ul Haq, Mazhar Javed Awan, Muhammad Imran, An Automatic Detection of Breast Cancer Diagnosis and Prognosis Based on Machine Learning Using Ensemble of Classifiers, 2022, 10, 2169-3536, 78242, 10.1109/ACCESS.2022.3174599
    47. Rayya A. Al-Balushi, Ashanul Haque, Mohd. Saeed, Thuraya Al-Harthy, Mohammed Al-Hinaai, Salim Al-Hashmi, Unlocking the Anticancer Potential of Frankincense Essential Oils (FEOs) Through Nanotechnology: A Review, 2024, 66, 1073-6085, 3013, 10.1007/s12033-023-00918-5
    48. Amal A. Alhaidary, Ahmad R. Al-Qudimat, Haitham Arabi, Raed M. Al-Zoubi, Imaging Patterns in Breast Cancer for Women Under 40 Years: A Descriptive Cohort Study, 2024, 14, 2210-6014, 63, 10.1007/s44197-023-00169-2
    49. Mohammed Ali Abutalib, Anwar Shams, Shadi Tamur, Eman A. Khalifa, Ghaliah Obaid Alnefaie, Yousef M. Hawsawi, Metastatic papillary thyroid carcinoma in pleural effusion: a case report and review of the literature, 2023, 17, 1752-1947, 10.1186/s13256-023-04265-6
    50. Muhannad Faleh Alanazi, Ashokkumar Thirunavukkarasu, Maily Alrowily, Nouf Alaqel, Abdulelah Alaqel, Mutlaq Alruwaili, Nouf Nashmi M Alazmi, Osamah Alhassan, Mona Fahad M Aljarallah, Afrah Mohaimeed Altaymani, A Cross-Sectional Evaluation of Knowledge About Breast Cancer and Perceived Barriers to the Uptake of Mammogram Screening Among Northern Saudi Women: A Population-Based Study, 2023, Volume 15, 1179-1314, 451, 10.2147/BCTT.S414635
    51. Meaad F Alatawi, Abdulaziz Al-Saif, Fahad D Alosaimi, Role of Psychosomatic Medicine in Complex Medical Cases: A Case Study of a Patient With Breast Cancer Who Refused Mastectomy, 2024, 2168-8184, 10.7759/cureus.61343
    52. Nawaf Alhindi, Basma Bamakhrama, Anas Alzahrani, Hatan Mortada, Nashwa M. Ali, Abdullah Alruwaili, Noor Baamir, Hattan Aljaaly, Risk factors of implant loss and complications post-implant based breast reconstruction: A meta-analysis, 2023, 46, 1435-0130, 865, 10.1007/s00238-023-02077-x
    53. Hanan A Albenayyan, Renad AlSubaie, Maryam O Alarfaj, Lames Alshekhmobarak, Mohammed F Alkhalifah, Hajar Alsaleem, Dalal Almulhim, Aisha A AlJughaiman, Fatimah A Albahrani, Almaha A Aleidan, Razan M Alzahrani, Lama Alobaid, Taghreed Alhinidi, Cancer Stigma Among 800 Saudi Citizens: A Cross-Sectional Study and Literature Review, 2023, 2168-8184, 10.7759/cureus.49088
    54. Musa AlHarbi, Nahla Ali Mobark, Wael Abdel Rahman AlJabarat, Hadeel ElBardis, Ebtehal AlSolme, Abdullah Bany Hamdan, Ali H. AlFakeeh, Fatimah AlMushawah, Fawz AlHarthi, Abdullah A. AlSharm, Ali Abdullah O. Balbaid, Naji AlJohani, Alicia Y. Zhou, Heather A. Robinson, Saleh A. Alqahtani, Malak Abedalthagafi, Investigating the prevalence of pathogenic variants in Saudi Arabian patients with familial cancer using a multigene next generation sequencing panel, 2023, 14, 1949-2553, 580, 10.18632/oncotarget.28457
    55. Badr Alharbi, Hatim S Alnosayan, Faisal Awadh Al-Harbi, Alwleed M Alaidah, Albaraa Nasser Almoshiqeh, Abdullah Mulfi Alharbi, Emad Alwashmi, Adil Khalaf Altwairgi, Epidemiology and Treatment Outcomes of Renal Cell Carcinoma in Qassim Region, Saudi Arabia: A Retrospective Study, 2024, 2168-8184, 10.7759/cureus.72748
    56. Mussab A Barkar, Zaher Mikwar, Adil A Khalid, Ali A Mohammedamin, Abdulrahman H Aloufi, Abdulmajeed A Abualhamail, Hamad A Alghashim, Patient Satisfaction and Quality of Life After Mastectomy at King Abdulaziz Medical City, Jeddah, 2023, 2168-8184, 10.7759/cureus.51029
    57. RUPA R, PAVITHRA B, KAVYA M, NIKHITHA K V, NIVETHA J D, Bindhu J, Evaluation of Anticancer Activity and Structural Analysis of Biosynthesized Silver Nanoparticles (AgNPs) from Centella Asiatica, 2024, 17, 0974-3278, 7256, 10.37285/ijpsn.2024.17.2.7
    58. Mahvish Khan, Nashwa Z.A. Bushara, Manoj Kumar, Raju K. Mandal, Saheem Ahmad, Saif Khan, Frequency of Healthy Control Genotype of VDR Gene Polymorphisms in the Saudi Population of the Ha'il Region: A Comparative Study with Worldwide Population , 2024, 43, 0731-8898, 61, 10.1615/JEnvironPatholToxicolOncol.2023048813
    59. Mohammed Omar, Ali Alnahdi, Psychometric Properties and Factorial Analysis of the Arabic McGill-QoL Questionnaire in Breast Cancer, 2023, Volume 15, 1179-1314, 813, 10.2147/BCTT.S422369
    60. Ghala Yasin, Abeer A Subke, Breast Cancer Screening Awareness and Associated Factors Among Saudi Females: A Cross-Sectional Study in Jeddah, Saudi Arabia (2024), 2024, 2168-8184, 10.7759/cureus.60337
    61. Mehenaz Hanbazazh, Abdulhadi Samman, Saad Samargandy, Jaudah Al-Maghrabi, Prognostic value of glucose transporter proteins-1 (GLUT1) in breast carcinoma, 2023, 18, 1993-2820, 10.1080/19932820.2023.2283953
    62. Ahmed Saad AL Zomia, Ibrahim Ali M AL Zehefa, Lama Ali Lahiq, Mohammed Tarek Mirdad, Abdullah Saad Alshahrani, Turki Alshahrani, Nawaf N. Almahfuth, Mahmoud Tarek Mirdad, Albara Awad Alqarni, Noor Mohamed Alshareef, Ryan M. AL Qahtani, Mohammed Abdulrahman Asiri, Mohammed Saad Alshahrani, Ramy Mohamed Ghazy, Ibrahim Tawhari, Tracking the epidemiological trends of female breast cancer in Saudi Arabia since 1990 and forecasting future statistics using global burden of disease data, time-series analysis, 2024, 24, 1471-2458, 10.1186/s12889-024-19377-x
    63. Ahmed M Badheeb, Fasal Ahmed, Musadag Elhadi, Nasher Alyami, Mohamed A Badheeb, Clinical and Therapeutic Profile of Non-Hodgkin’s Lymphoma: A Retrospective Study From a Najran Oncology Center, 2023, 2168-8184, 10.7759/cureus.40125
    64. Mohmmed M. Aljeldah, Talat A. El-kersh, Mourad A.M. Aboul-Soud, Parasporins of Bacillus thuringiensis Strain Exhibit Apoptosis-Mediated Selective Cytotoxicity to MDA-MB-231 Cells through Oxidative Stress, 2024, 18, 09737510, 1305, 10.22207/JPAM.18.2.51
    65. Jehad Alzahrani, Suhaib Radi, Abdullah Aljabri, Mohammad Alandejani, Advanced Unresectable Differentiated Thyroid Cancer With Anaplastic Transformation: A Case Report and Review of the Literature, 2024, 2168-8184, 10.7759/cureus.73956
    66. Moath A. Alfaleh, Omar A. Alanzi, Mohammed F. Alzamil, Fatmah A. Alabdulwahid, Turki M. AlMuhaimid, Association Between Vitamin D Deficiency and Papillary Thyroid Cancer: Tertiary Center Experience, 2024, 2231-3796, 10.1007/s12070-024-05225-2
    67. Dalia A. Elmaghraby, Ahmad Mohammed Al ben Hamad, Khalid Mohammed Alhunfoosh, Hamzah Redha Alturifi, Mohammed Abdullah Albahrani, Ahmed Ali Alshalla, Anas Alyahyan, Muntathir Altaweel, Exploration and Assessment of Breast Cancer Awareness in the Saudi Population: A Cross-Sectional Study, 2023, 50, 0390-6663, 10.31083/j.ceog5011245
    68. Ahmed M. Aljameeli, Most Prevalent Cancer Subtypes in Saudi Arabia, 2024, 0974-360X, 5457, 10.52711/0974-360X.2024.00835
    69. Abdullah U. Althemery, Rawan Alzahrani, Nura Alajlan, Abdullah M. Alrajhi, Quality of life for patients on oncology treatments in the Kingdom of Saudi Arabia: a systematic review, 2025, 18, 2052-3211, 10.1080/20523211.2024.2449036
    70. F. H. Khathayer, M. H. Mikael, S. Z. Kadhim, Epidemiology of the most Prevalent Cancers in Ninewa between 2017–2021, 2025, 23, 2619-0494, 34, 10.31631/2073-3046-2024-23-6-34-46
    71. Waad Moied Althaqfi, Shahad Hassan Alshahrani, Mjd Mohammed Alanazi, Rahaf Ali Sharahili, Mona Qushawy, Yasmin Mortagi, Huda M. Atif, Kousalya Prabahar, Mansuor A. Alanazi, Mody Albalawi, Zuhair M. Mohammedsaleh, Rehab Ahmed, Nehal Elsherbiny, Development and optimization of flaxseed oil nanoemulsions: implications for ulcerative colitis treatment, 2025, 0193-2691, 1, 10.1080/01932691.2025.2456530
    72. Faisal Aljadani, Reem Nughays, Ghaida Alharbi, Enar Almazroy, Shahad Elyas, Hala Danish, Rimaz Alanazi, Badr Aldrees, Galia Jadkarim, Zaher Mikwar, Quality of Life in Breast Cancer Patients in Saudi Arabia: A Systematic Review, 2025, Volume 17, 1179-1314, 171, 10.2147/BCTT.S505725
    73. Mansour Alsaleem, Samar Sindi, Safiah Alhazmi, Sabah Hassan, Magdah Ganash, Najla Alburae, Shadi Alkhayyat, Ayman Linjawi, Aisha Elaimi, Saif A. Alharthy, Khloud Algothmi, Reem Farsi, Ghadeer Alrefaei, Nouf Alsubhi, Norah Hamdi, Heba Alkhatabi, Deciphering the prognostic impact of aberrant DNA methylation on ANGPT1 gene in breast cancer, 2025, 15, 2045-2322, 10.1038/s41598-025-90001-7
    74. Doha Mohammed Rayed Fatani, Tusneem Elhassan, Narmeen Shaikh, Noara Alhusseini, Linking local cancer registries and national death records: a crucial step for accurate survival data in Saudi Arabia, 2025, 25, 1472-6963, 10.1186/s12913-025-12716-7
  • Reader Comments
  • © 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(5601) PDF downloads(1000) Cited by(5)

Figures and Tables

Figures(12)  /  Tables(7)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog