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

Kesici, E., Pelloni, B., Pryer, T. and Smith, D. (2018) A numerical implementation of the unified Fokas transform for evolution problems on a finite interval. European Journal of Applied Mathematics, 29 (3). pp. 543-567. ISSN 1469-4425

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To link to this item DOI: 10.1017/S0956792517000316

Abstract/Summary

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. To our knowledge, the numerical evaluation of the solution so far could only be obtained by a time-stepping scheme, that must also take into account the issue, generically non-trivial, of the imposition of the boundary conditions. Instead of computing the evolution numerically, we evaluate the novel solution representation formula obtained by the unified transform, also known as Fokas transform. 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.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:72115
Publisher:Cambridge University Press

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