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Computation of Mixed Type Functional Differential Boundary Value Problems
Abell, Kate A. Elmer, Christopher E. Humphries, A. R. Van Vleck, Erik S.
Abell, Kate A.
Elmer, Christopher E.
Humphries, A. R.
Van Vleck, Erik S.
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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.
Description
This is the published version, also available here: http://dx.doi.org/10.1137/040603425.
Date
2005-09-05
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Publisher
Society for Industrial and Applied Mathematics
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Keywords
mixed type functional differential equations, Boundary value problems, traveling waves, collocation
Citation
Abell, Kate A., Elmer, Christopher E., Humphries, A. R., Van Vleck, Erik. "Computation of Mixed Type Functional Differential Boundary Value Problems." (2005) SIAM J. Appl. Dyn. Syst., 4(3), 755–781. (27 pages). http://dx.doi.org/10.1137/040603425.