A numerical implementation of the unified Fokas transform for evolution problems on a finite interval
| Autor: | Emine Kesici, David A. Smith, Beatrice Pelloni, Tristan Pryer |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
math.NA
Applied Mathematics Complex line 010102 general mathematics Mathematical analysis Order (ring theory) Interval (mathematics) Numerical Analysis (math.NA) Deformation (meteorology) 01 natural sciences 010101 applied mathematics Third order Mathematics - Analysis of PDEs Scheme (mathematics) FOS: Mathematics Mathematics - Numerical Analysis Boundary value problem 0101 mathematics Representation (mathematics) math.AP Mathematics Analysis of PDEs (math.AP) |
| Zdroj: | Kesici, E, Pelloni, B, Pryer, T & Smith, D 2018, ' A numerical implementation of the unified Fokas transform for evolution problems on a finite interval ', European Journal of Applied Mathematics, vol. 29, no. 3, pp. 543-567 . https://doi.org/10.1017/S0956792517000316 |
| ISSN: | 1469-4425 |
| DOI: | 10.1017/S0956792517000316 |
| Popis: | We present the numerical solution of two-point boundary value problems for a third order linear PDE, representing a linear evolution in one space dimension. The difficulty of this problem is in the numerical imposition of the boundary conditions, and to our knowledge, no such computations exist. Instead of computing the evolution numerically, we evaluate the solution representation formula obtained by the unified transform of Fokas. This representation involves complex line integrals, but in order to evaluate these integrals numerically, it is necessary to deform the integration contours using appropriate deformation mappings. We formulate a strategy to implement effectively this deformation, which allows us to obtain accurate numerical results. Comment: 20 pages, 14 figures |
| Databáze: | OpenAIRE |
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