A simple solution of the Bratu problem

被引：66
作者：
Mohsen, A. [1 ]
机构：
[1] Cairo Univ, Fac Engn, Dept Engn Math & Phys, Giza 12211, Egypt
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2014年 / 67卷 / 01期
关键词：
Bratu's problem; Nonlinear partial differential equations; Standard finite difference; Nonstandard finite difference; BOUNDARY-VALUE-PROBLEMS; POSITIVE SOLUTIONS; NONLINEAR-SYSTEMS; ANALYTIC APPROACH; SPLINE METHOD; CONTINUATION; BIFURCATION; EXISTENCE; EQUATIONS;
D O I：
10.1016/j.camwa.2013.10.003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A brief survey of the properties and different treatments of the one-dimensional (1D) and (2D) Bratu problems is presented. Different iterative treatments of the resulting nonlinear system of equations are discussed. The finite-difference treatment of the problem is considered. Nonstandard finite-difference methods with a simple sinusoidal starting function having an appropriate amplitude are recommended. Bounds on the amplitude for yielding both lower and upper solutions are given. (C) 2013 Elsevier Ltd. All rights reserved.
引用
收藏
页码：26 / 33
页数：8
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