Computation of mixed type functional differential boundary value problems

Document Type

Article

Publication Date

12-1-2005

Abstract

We study boundary value differential-difference equations where the difference terms may contain both advances and delays. Special attention is paid to connecting orbits, in particular to the modeling of the tails after truncation to a finite interval, and we reformulate these problems as functional differential equations over a bounded domain. Connecting orbits are computed for several such problems including discrete Nagumo equations, an Ising model, and Frenkel-Kontorova type equations. We describe the collocation boundary value problem code used to compute these solutions, and the numerical analysis issues which arise, including linear algebra, boundary functions and conditions, and convergence theory for the collocation approximation on finite intervals. © 2005 Society for Industrial and Applied Mathematics.

Identifier

21244461900 (Scopus)

Publication Title

SIAM Journal on Applied Dynamical Systems

External Full Text Location

https://doi.org/10.1137/040603425

e-ISSN

15360040

ISSN

15360040

First Page

755

Last Page

781

Issue

3

Volume

4

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