A variant of Newton's method for the computation of traveling waves of bistable differential-difference equations

被引：50
作者：
Elmer C.E. [1 ]
Van Vleck E.S. [2 ]
机构：
[1] Department of Mathematical Sciences, New Jersey Institute of Technology, Newark
[2] Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden
来源：
Journal of Dynamics and Differential Equations | 2002年 / 14卷 / 3期
基金：
美国国家科学基金会;
关键词：
Mixed type functional differential equations; Newton's method; Traveling waves;
D O I：
10.1023/A:1016386414393
中图分类号：
学科分类号：
摘要：
We consider a variant of Newton's method for solving nonlinear differential-difference equations arising from the traveling wave equations of a large class of nonlinear evolution equations. Building on the Fredholm theory recently developed by Mallet-Paret we prove convergence of the method. The utility of the method is demonstrated with a series of examples. © 2002 Plenum Publishing Corporation.
引用
收藏
页码：493 / 517
页数：24
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