A robust adaptive grid method for a nonlinear singularly perturbed differential equation with integral boundary condition

被引：0
作者：
Li-Bin Liu
Guangqing Long
Zhongdi Cen
机构：
[1] Nanning Normal University,School of Mathematics and Statistics
[2] Zhejiang Wanli University,Institute of Mathematics
来源：
Numerical Algorithms | 2020年 / 83卷
关键词：
Singularly perturbed; Adaptive grid method; Integral boundary condition; Monitor function;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, the numerical solution of a nonlinear first-order singularly perturbed differential equation with integral boundary condition is considered. The discrete method is generated by a backward Euler formula and the grid is obtained by equidistributing a monitor function based on arc-length. We first give a rigorous error analysis for the numerical method of this problem on a grid that is constructed adaptively from a knowledge of the exact solution. A first-order rate of convergence, independent of the perturbation parameter, is established. Then, an a posteriori error bound and the corresponding convergence result are derived for the presented numerical scheme on an adaptive grid, which is constructed adaptively from a discrete approximation of the exact solution. At last, numerical experiments are given to illustrate our theoretical results.
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页码：719 / 739
页数：20
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