Numerical treatment of singularly perturbed parabolic partial differential equations with nonlocal boundary condition

被引:3
作者
Wondimu, Getu Mekonnen [1 ]
Woldaregay, Mesfin Mekuria [1 ]
Dinka, Tekle Gemechu [1 ]
Duressa, Gemechis File [2 ]
机构
[1] Adama Sci & Technol Univ, Dept Appl Math, Adama, Ethiopia
[2] Jimma Univ, Dept Math, Jimma, Ethiopia
关键词
singularly perturbed problems; partial differential equations; reaction-diffusion; method of lines; uniform convergence; nonlocal boundary condition; CONVECTION-DIFFUSION TYPE; SCHEME;
D O I
10.3389/fams.2022.1005330
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
This paper presents numerical treatments for a class of singularly perturbed parabolic partial differential equations with nonlocal boundary conditions. The problem has strong boundary layers at x = 0 and x = 1. The nonstandard finite difference method was developed to solve the considered problem in the spatial direction, and the implicit Euler method was proposed to solve the resulting system of IVPs in the temporal direction. The nonlocal boundary condition is approximated by Simpsons 1/3 rule. The stability and uniform convergence analysis of the scheme are studied. The developed scheme is second-order uniformly convergent in the spatial direction and first-order in the temporal direction. Two test examples are carried out to validate the applicability of the developed numerical scheme. The obtained numerical results reflect the theoretical estimate.
引用
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页数:11
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