A numerical implementation of the unified Fokas transform for evolution problems on a finite interval

Emine Kesici, Beatrice Pelloni, Tristan Pryer, David Smith

Research output: Contribution to journalArticle

3 Citations (Scopus)
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Abstract

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.
Original languageEnglish
Pages (from-to)543-567
Number of pages25
JournalEuropean Journal of Applied Mathematics
Volume29
Issue number3
Early online date23 Nov 2017
DOIs
Publication statusPublished - 1 Jun 2018

Keywords

  • math.NA
  • math.AP

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