Computation of Mixed Type Functional Differential Boundary Value Problems

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Issue Date
2005-09-05Author
Abell, Kate A.
Elmer, Christopher E.
Humphries, A. R.
Van Vleck, Erik S.
Publisher
Society for Industrial and Applied Mathematics
Type
Article
Article Version
Scholarly/refereed, publisher version
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Show full item recordAbstract
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.
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This is the published version, also available here: http://dx.doi.org/10.1137/040603425.
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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.
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