An efficient adaptive grid method for a system of singularly perturbed convection-diffusion problems with Robin boundary conditions

Advances in Difference Equations

article

Liu, Li-Bin¹  Liang, Ying¹  Bao, Xiaobing²  Fang, Honglin¹ 

[1] School of Mathematics and Statistics, Nanning Normal University;School of Big Data and Artificial Intelligence, Chizhou University

关键词: Singularly perturbed;    Convection-diffusion problem;    Robin boundary conditions;    Adaptive grid;   

DOI  :  10.1186/s13662-020-03166-y

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

A system of singularly perturbed convection-diffusion equations with Robin boundary conditions is considered on the interval$[0,1]$ . It is shown that any solution of such a problem can be expressed to a system of first-order singularly perturbed initial value problem, which is discretized by the backward Euler formula on an arbitrary nonuniform mesh. An a posteriori error estimation in maximum norm is derived to design an adaptive grid generation algorithm. Besides, in order to establish the initial values of the original problems, we construct a nonlinear optimization problem, which is solved by the Nelder–Mead simplex method. Numerical results are given to demonstrate the performance of the presented method.

【 授权许可】

CC BY