Solving a second-order nonlinear singular perturbation ordinary differential equation by a Samarskii scheme

被引：5
|
作者：
Zadorin A.I. [1 ]
Tikhovskaya S.V. [1 ]
机构：
[1] Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, ul. Pevtsova 13, Omsk
来源：
Zadorin, A. I. (zadorin@ofim.oscsbras.ru) | 1600年 / Maik Nauka Publishing / Springer SBM卷 / 06期
基金：
俄罗斯基础研究基金会;
关键词：
Newton method; Picard method; Samarskii scheme; second-order nonlinear ordinary differential equation; Shishkin grid; singular perturbation; two-grid algorithm; uniform convergence;
D O I：
10.1134/S1995423913010023
中图分类号：
学科分类号：
摘要：
A boundary value problem for a second-order nonlinear singular perturbation ordinary differential equation is considered. A method based on Newton and Picard linearizations using a modified Samarskii scheme on a Shishkin grid for a linear problem is proposed. It is proved that the difference schemes are of second-order and uniformly convergent. To decrease the number of arithmetic operations, a two-grid method is proposed. The results of some numerical experiments are discussed. © 2013 Pleiades Publishing, Ltd.
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页码：9 / 23
页数：14
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