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A 6-point subdivision scheme and its applications for the solution of 2nd order nonlinear singularly perturbed boundary value problems

1 Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan
2 Department of Mathematics, Cankaya University, Ankara 06530, Turkey
3 Institute of Space Sciences, 077125 Magurele-Bucharest, Romania
4 Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
5 Department of Mathematics, The Government Sadiq College Women University, Bahawalpur 63100, Pakistan
6 Institute of IR 4.0, The National University of Malaysia, 43600 UKM, Bangi, Selangor, Malaysia
7 Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey
8 Department of Law, Economics and Human Sciences & Decisions Lab, University Mediterranea of Reggio Calabria, Reggio Calabria, Italy

Special Issues: Numerical Linear Algebra for Large-Scale Dynamical Systems

In this paper, we first present a 6-point binary interpolating subdivision scheme (BISS) which produces a C2 continuous curve and 4th order of approximation. Then as an application of the scheme, we develop an iterative algorithm for the solution of 2nd order nonlinear singularly per-turbed boundary value problems (NSPBVP). The convergence of an iterative algorithm has also been presented. The 2nd order NSPBVP arising from combustion, chemical reactor theory, nuclear engi-neering, control theory, elasticity, and fluid mechanics can be solved by an iterative algorithm with 4th order of approximation.
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Keywords subdivision schemes; interpolation; approximation; Singularly perturbed boundary value problem; iterative algorithm

Citation: Ghulam Mustafa, Dumitru Baleanu, Syeda Tehmina Ejaz, Kaweeta Anjum, Ali Ahmadian, Soheil Salahshour, Massimiliano Ferrara. A 6-point subdivision scheme and its applications for the solution of 2nd order nonlinear singularly perturbed boundary value problems. Mathematical Biosciences and Engineering, 2020, 17(6): 6659-6677. doi: 10.3934/mbe.2020346


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