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: J.J.H.Miller R.Ishwariya S.Valarmathi
• 来源期刊: 生物数学学报:英文版
• 学科: 工学
• 关键词: Singular PERTURBATIONS BOUNDARY layers linear parabolic differential equations Robin BOUNDARY conditions finite difference schemes Shishkin MESHES PARAMETER UNIFORM convergence
• 年，卷（期）: 2019,（1）
• 页码范围: 1-31
• 页数: 31页
• 分类号: TP312

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.