Research article Special Issues

Numerical solutions of 2D Fredholm integral equation of first kind by discretization technique

  • Received: 18 October 2019 Accepted: 27 February 2020 Published: 02 March 2020
  • MSC : 65A05, 65G99, 65R20

  • A novel numerical technique to solve 2D Fredholm integral equations (2DFIEs) of first kind is proposed in this study. This technique is based on the discretization of 2DFIEs by replacing the unknown function with two-dimensional Bernstein polynomial basis functions. We formulate the convergence analysis which shows the fast converges of this technique to the actual solution. Some problems of 2D linear Fredholm integral equations are illustrated to show the efficiency of the proposed scheme.

    Citation: Faheem Khan, Tayyaba Arshad, Abdul Ghaffar, Kottakkaran Sooppy Nisar, Devendra Kumar. Numerical solutions of 2D Fredholm integral equation of first kind by discretization technique[J]. AIMS Mathematics, 2020, 5(3): 2295-2306. doi: 10.3934/math.2020152

    Related Papers:

  • A novel numerical technique to solve 2D Fredholm integral equations (2DFIEs) of first kind is proposed in this study. This technique is based on the discretization of 2DFIEs by replacing the unknown function with two-dimensional Bernstein polynomial basis functions. We formulate the convergence analysis which shows the fast converges of this technique to the actual solution. Some problems of 2D linear Fredholm integral equations are illustrated to show the efficiency of the proposed scheme.


    加载中


    [1] J. P. Kauthen, Continuous time collocation methods for Volterra-Fredholm integral equations, Numeriche Math., 5 (1989), 409-424.
    [2] F. Khan, G. Mustafa, M. Omar, et al., Numerical approach based on Bernstein polynomials for solving mixed Volterra-Fredholm integral equations, AIP Adv., 7 (2017), 125123.
    [3] M. M. Mustafa, N. I. Ghanim, Numerical solution of linear Volterra-Fredholm integral equations using Lagrange polynomials, Math. Theory Model., 4 (2014), 158-167.
    [4] A. Alipanah, S. Esmaeili, Numerical solution of the two-dimensional Fredholm integral equations using Gaussian radial basis function, J. Comput. Appl. Math., 235 (2011), 5342-5347. doi: 10.1016/j.cam.2009.11.053
    [5] C. Heitzinger, A. Hössinger, S. Selberherr, An algorithm for the smoothing three-dimensional monte carlo ion implantation simulation results, Proc. 4th Mathmod Vienna, (2003), 702-711.
    [6] A. Fallahzadeh, Solution of two-dimensional Fredholm integral equation via RBF-triangular method, J. Interpolat. Approx. Sci. Comput., 12 (2012), Article ID jiasc-00002.
    [7] F. Khan, M. Omar, Z. Ullah, Discretization method for the numerical solution of 2D Volterra integral equation based on two-dimensional Bernstein polynomial, AIP Adv., 8 (2018), 125209.
    [8] F. H. Shekarabi, K. Maleknejad, R. Ezzati, Application of two-dimensional Bernstein polynomials for solving mixed Volterra Fredholm integral equations, Afr. Mat., 26 (2015), 1237-1251. doi: 10.1007/s13370-014-0283-6
    [9] A. Tari, S. Shahmorad, A computational method for solving two-dimensional linear Fredholm integral equations of the second kind, ANZIAM J., 49 (2008), 543-549. doi: 10.1017/S1446181108000126
    [10] W. J. Xie, F. R. Lin, A fast numerical solution method for two dimensional Fredholm integral equations of the second kind, Appl. Numer. Math., 59 (2009), 1709-1719. doi: 10.1016/j.apnum.2009.01.009
    [11] H. Guoqiang, W. Jiong, Extrapolation of Nystrom solution for two dimensional nonlinear Fredholm integral equations, J. Comput. Appl. Math., 134 (2001), 259-268. doi: 10.1016/S0377-0427(00)00553-7
    [12] X. Wang, R. A Wildman, D. S Weile, et al., A finite difference delay modeling approach to the discretization of the time domain integral equations of electromagnetics, IEEE Trans. Antennas Propag., 8 (2008), 2442-2452.
    [13] T. N. Narasimhan, P. A. Witherspoon, An integrated finite difference method for analyzing fluid flow in porous media, Water Resorces Res., 12 (1976), 57-64. doi: 10.1029/WR012i001p00057
    [14] M. Jalalvanda, B. Jazbib, M. R. Mokhtarzadehc, A finite difference method for the smooth solution of linear volterra integral equations, Int. J. Nonlinear Anal. Appl., 2 (2013), 1-10.
    [15] A. Khalid, M. N. Naeem, Z. Ullah, et al., Numerical solution of the boundary value problems arising in magnetic fields and cylindrical shells, Mathematics, 7 (2019), doi:10.3390/math7060508.
    [16] S. S. Ray, Om P. Agrawal, R. K. Bera, et al., Analytical and numerical methods for solving partial differential equations and integral equations arising in Physical Models, Abstr. Appl. Anal., 14 (2014), Available from: https://doi.org/10.1155/2014/635235.
    [17] A. Shaikh, A. Tassaddiq, K. S. Nisar, et al., Analysis of differential equations involving CaputoFabrizio fractional operator and its applications to reaction diffusion equations, Adv. Difference Equ., 178 (2019), Available from: https://doi.org/10.1186/s13662-019-2115-3.
    [18] A. Shaikh, K. S Nisar, Transmission dynamics of fractional order Typhoid fever model using CaputoFabrizio operator, Chaos Solitons Fractals, 128 (2019), 355-365. doi: 10.1016/j.chaos.2019.08.012
    [19] M. Khader, K. M. Saad, A numerical study using Chebyshev collocation method for a problem of biological invasion: Fractional Fisher equation, Int. J. Biomath., 11 (2018), Available from: https://doi.org/10.1142/S1793524518500997.
    [20] J. F. Aguiler, K. M. Saad, D. Baleanu, Fractional dynamics of an erbium-doped fiber laser model, Opt. Quantum Electron., 51 (2019), Available from: https://doi.org/10.1007/s11082-019-2033-3.
  • Reader Comments
  • © 2020 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(4099) PDF downloads(1049) Cited by(3)

Article outline

Figures and Tables

Figures(3)  /  Tables(3)

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog