Analysis and Computation of Travelling Wave Solutions of Bistable Differential-Difference Equations
C E. Elmer, E S. Vanleck
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.