Elmer, C.
and Vanleck, E.
(1999),
Analysis and Computation of Travelling Wave Solutions of Bistable Differential-Difference Equations, Nonlinearity
(Accessed July 2, 2025)
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Analysis and Computation of Travelling Wave Solutions of Bistable Differential-Difference Equations
Published
Author(s)
, 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
Pub Type
Journals
Keywords
Lattice differential equations, Newton's method, traveling waves
Citation
Issues
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Created July 1, 1999, Updated June 2, 2021