A parameter uniform essentially firsorder convergent numerical method for a parabolic system of singularly perturbed differential equations of reaction—diffusion type with initial and Robin boundary conditions  

作　　者：R.Ishwariya J.J.H.Miller S.Valarmathi 

机构地区：[1]Department of Mathematics,Bishop Heber College Tiruchirappalli,Tamil Nadu,India [2]Institute for Numerical Computation and A nalysis Dublin,Ireland

出　　处：《International Journal of Biomathematics》2019年第1期1-31,共31页生物数学学报（英文版）

摘　　要：In this paper,a class of linear parabolic systems of singularly perturbed second-order differential equations of reaction-diffusion type with initial and Robin boundary conditions is considered.The components of the solution u→ of this system are smooth,whereas the components of αu→/αx exhibit parabolic boundary layers.A numerical method composed of a classical finite difference scheme on a piecewise uniform Shishkin mesh is suggested.This method is proved to be first-order convergent in time and essentially first-order convergent in the space variable in the maximum norm uniformly in the perturbation parameters.

关 键 词：Singular perturbations BOUNDARY layers linear parabolic differential equations Robin BOUNDARY conditions finite difference schemes Shishkin MESHES PARAMETER UNIFORM convergence 

分 类 号：TP312[自动化与计算机技术—计算机软件与理论]