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A Variant of Newton's Method for the Computation of Traveling Waves of Bistable Differential-Difference Equations

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey, 07102

    Christopher E. Elmer

  2. Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, Colorado, 80401

    Erik S. Van Vleck

Authors
  1. Christopher E. Elmer
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  2. Erik S. Van Vleck
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Elmer, C.E., Van Vleck, E.S. A Variant of Newton's Method for the Computation of Traveling Waves of Bistable Differential-Difference Equations. Journal of Dynamics and Differential Equations 14, 493–517 (2002). https://doi.org/10.1023/A:1016386414393

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