Spline approximation method for singularly perturbed differential-difference equation on nonuniform grids

作     者：P.Mushahary S.R.Sahu J.Mohapatra 

作者机构：Department of Mathematics National Institute of Technology RourkelaIndia 

出 版 物：《International Journal of Modeling, Simulation, and Scientific Computing》 (建模、仿真和科学计算国际期刊（英文）)

年 卷 期：2021年第12卷第1期

页      面：213-228页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：The work is supported by DST Government of India under Grant No.EMR/2016/005805 

主　　题：Singular perturbation mixed shift cubic spline Bakhvalov-Shishkin mesh Vulanovi′c mesh finite difference scheme 

摘      要：In this paper,a second-order singularly perturbed differential-difference equation involving mixed shifts is *** first,through Taylor series approximation,the original model is reduced to an equivalent singularly perturbed differential ***,the model is treated by using the hybrid finite difference scheme on different types of layer adapted meshes like Shishkin mesh,Bakhvalov–Shishkin mesh and Vulanovi′c ***,the hybrid scheme consists of a cubic spline approximation in the fine mesh region and a midpoint upwind scheme in the coarse mesh *** error analysis is carried out and it is shown that the proposed scheme is of second-order convergence irrespective of the perturbation *** display the efficacy and accuracy of the proposed scheme,some numerical experiments are presented which support the theoretical results.