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

DOI10.1017/S0956792517000316zbMath1394.65120arXiv1610.04509OpenAlexW2538032414MaRDI QIDQ4575293

Tristan Pryer, Emine Kesici, Beatrice Pelloni, David Andrew Smith

Publication date: 13 July 2018

Published in: European Journal of Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.04509

zbMATH Keywords

initial boundary value problemsAiry equationunified transformFokas transformnon-periodic problems

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Transform methods (e.g., integral transforms) applied to PDEs (35A22) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99)

Related Items (9)

Fundamental solutions of the fractional Fresnel equation in the real half-line ⋮ The numerical solution of semidiscrete linear evolution problems on the finite interval using the Unified Transform Method ⋮ Integral representations for the double-diffusivity system on the half-line ⋮ Boundary behavior of the solution to the linear Korteweg‐De Vries equation on the half line ⋮ Fokas method for the heat equation on metric graphs ⋮ The design of conservative finite element discretisations for the vectorial modified KdV equation ⋮ Conservative Galerkin methods for dispersive Hamiltonian problems ⋮ Revivals and fractalisation in the linear free space Schrödinger equation ⋮ Fokas diagonalization of piecewise constant coefficient linear differential operators on finite intervals and networks

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Evolution PDEs and augmented eigenfunctions. half-line
• Novel numerical techniques based on Fokas transforms, for the solution of initial boundary value problems
• Evolution PDEs and augmented eigenfunctions. Finite interval
• Talbot quadratures and rational approximations
• Well-posed two-point initial-boundary value problems with arbitrary boundary conditions
• The solution of linear constant-coefficient evolution PDEs with periodic boundary conditions
• The Exponentially Convergent Trapezoidal Rule
• A Unified Approach to Boundary Value Problems
• Dispersive Quantization
• Well-posed boundary value problems for linear evolution equations on a finite interval
• Unified Transform for Boundary Value Problems
• A hybrid analytical–numerical method for solving evolution partial differential equations. I. The half-line
• Gibbs Phenomenon for Dispersive PDEs on the Line
• The spectral representation of two-point boundary-value problems for third-order linear evolution partial differential equations
• A transform method for linear evolution PDEs on a finite interval

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