A spectrally accurate numerical implementation of the Fokas transform method for Helmholtz-type PDEs

DOI10.1080/17476933.2013.766883zbMath1291.65083OpenAlexW2161325327MaRDI QIDQ5417849

Christopher-Ian Raphaël Davis, Bengt Fornberg

Publication date: 22 May 2014

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17476933.2013.766883

zbMATH Keywords

boundary integral methodpolygonal domainLegendre polynomialsDirichlet-to-Neumann mapHelmholtz-type equationsFokas transform method

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Integral representations of solutions to PDEs (35C15) General theory of numerical methods in complex analysis (potential theory, etc.) (65E05) Numerical methods for integral transforms (65R10) Integral representations, integral operators, integral equations methods in two dimensions (31A10)

Related Items (10)

Numerical analysis of Fokas' unified method for linear elliptic PDEs ⋮ A hybrid method for solving inhomogeneous elliptic PDEs based on Fokas method ⋮ Computing eigenvalues and eigenfunctions of the Laplacian for convex polygons ⋮ A Survey of Trefftz Methods for the Helmholtz Equation ⋮ The Unified Transform and the Water Wave Problem ⋮ A Hybrid Analytical-Numerical Technique for Elliptic PDEs ⋮ An iterative spatial-stepping numerical method for linear elliptic PDEs using the unified transform ⋮ A class of unified transform techniques for solving linear elliptic PDEs in convex polygons ⋮ Water waves with moving boundaries ⋮ On the Fokas method for the solution of elliptic problems in both convex and non-convex polygonal domains

Cites Work

• An analytical method for linear elliptic PDEs and its numerical implementation
• On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals
• The generalized Dirichlet-Neumann map for linear elliptic PDEs and its numerical implementation
• Lax pairs and a new spectral method for linear and integrable nonlinear PDEs
• Two–dimensional linear partial differential equations in a convex polygon
• A spectral collocation method for the Laplace and modified Helmholtz equations in a convex polygon
• A numerical implementation of Fokas boundary integral approach: Laplace's equation on a polygonal domain
• A Unified Approach to Boundary Value Problems
• A unified transform method for solving linear and certain nonlinear PDEs
• A new transform method for evolution partial differential equations
• A hybrid analytical–numerical method for solving evolution partial differential equations. I. The half-line

This page was built for publication: A spectrally accurate numerical implementation of the Fokas transform method for Helmholtz-type PDEs