Monotone iterative technique for numerical solutions of fourth-order nonlinear elliptic boundary value problems

被引：11

作者：

Wang, Yuan-Ming ^{[1
]}

机构：

[1] E China Normal Univ, Dept Math, Shanghai 200062, Peoples R China

[2] Shanghai Normal Univ, E Inst Shanghai Univ, Div Computat Sci, Shanghai 200234, Peoples R China

来源：

APPLIED NUMERICAL MATHEMATICS | 2007年 / 57卷 / 10期

基金：

中国国家自然科学基金;

关键词：

founh-order elliptic equations; finite difference systems; monotone iterations; upper and lower solutions; rate of convergence;

D O I：

10.1016/j.apnum.2006.10.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with finite difference solutions of a class of fourth-order nonlinear elliptic boundary value problems. The nonlinear function is not necessarily monotone. A new monotone iterative technique is developed, and three basic monotone iterative processes for the finite difference system are constructed. Several theoretical comparison results among the various monotone sequences are given. A simple and easily verified condition is obtained to guarantee a geometric convergence of the iterations. Numerical results for a model problem with known analytical Solution are given. (c) 2006 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：1081 / 1096

页数：16

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