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Analysis and Computation of Travelling Wave Solutions of Bistable Differential-Difference Equations

Published

Author(s)

C E. Elmer, E S. Vanleck

Abstract

We consider a variant of Newton's method for solving nonlinear differential-difference equations arising from traveling wave equations of large class of nonlinear evolution equations. Using the Fredholm theory developed by J. Mallet-Paret we prove convergence of the method. Several examples are considered and the utility of the method is shown with a series of numerical experiments.
Citation
Nonlinearity
Volume
12
Issue
No. 4

Keywords

Lattice differential equations, Newton's method, traveling waves

Citation

Elmer, C. and Vanleck, E. (1999), Analysis and Computation of Travelling Wave Solutions of Bistable Differential-Difference Equations, Nonlinearity (Accessed February 28, 2024)
Created July 1, 1999, Updated June 2, 2021