A Difference Scheme of the Decomposition Method for an Initial Boundary Value Problem for the Singularly Perturbed Transport Equation

作     者：Shishkin, G., I Shishkina, L. P. 

作者机构：Russian Acad Sci Inst Math & Mech Ural Branch Ekaterinburg 620108 Russia 

出 版 物：《COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS》 (计算数学与数学物理学杂志)

年 卷 期：2022年第62卷第7期

页      面：1193-1201页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 0702[理学-物理学] 

基　　金：Russian Foundation of Basic Research [20-01-00650] 

主　　题：transport equation singularly perturbed initial boundary value problem boundary layer standard difference scheme decomposition of solution uniform grid epsilon-uniform convergence maximum norm continual approximation of solution 

摘      要：An initial boundary value problem for the singularly perturbed transport equation is considered. A new approach to constructing the difference scheme based on a special decomposition of solution into the sum of a regular and a singular components is proposed. A difference scheme is constructed based on the solution decomposition method in which the regular and singular components of the solution are considered on uniform grids, and their epsilon-uniform convergence in the maximum norm with the first order of the convergence rate is proved. Given the grid solutions for the components, a continual solution that approximates the solution of the initial boundary value problem for the singularly perturbed transport equation is constructed, and its epsilon-uniform convergence in the maximum norm with the first order of the convergence rate is proved. The proposed approach will make it possible to use the technique of improving the convergence rate of grid solutions on embedded grids for constructing difference schemes that converge epsilon-uniformly with the second-order rate and higher for the initial boundary value problem for the singularly perturbed transport equation.