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.

引用

页码：9 / 23

页数：14

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