Numerical analysis of Fokas' unified method for linear elliptic PDEs

DOI10.1016/j.apnum.2015.06.003zbMath1336.65183OpenAlexW819900212MaRDI QIDQ268860

K. M. Crooks, Anthony C. L. Ashton

Publication date: 15 April 2016

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2015.06.003

zbMATH Keywords

convergenceboundary integral methodconvex polygonnonlinear eigenvalue problemLaplacianGalerkin schemeHelmholtz operatorelliptic boundary value problemsemi-Fredholm operatorDirichlet eigenvalue problemDirichlet-Neumann mapunified method

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Nonlinear spectral theory, nonlinear eigenvalue problems (47J10) Numerical solutions to equations with nonlinear operators (65J15) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Boundary element methods for boundary value problems involving PDEs (65N38) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

Related Items (6)

Computing eigenvalues and eigenfunctions of the Laplacian for convex polygons ⋮ Integral representations for the double-diffusivity system on the half-line ⋮ A Hybrid Analytical-Numerical Technique for Elliptic PDEs ⋮ A class of unified transform techniques for solving linear elliptic PDEs in convex polygons ⋮ Solving PDEs of fractional order using the unified transform method ⋮ On the Fokas method for the solution of elliptic problems in both convex and non-convex polygonal domains

Cites Work

• Elliptic PDEs with constant coefficients on convex polyhedra via the unified method
• An analytical method for linear elliptic PDEs and its numerical implementation
• The generalized Dirichlet-Neumann map for linear elliptic PDEs and its numerical implementation
• Perturbation theory for linear operators.
• 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
• On the discrete approximation of eigenvalue problems with holomorphic parameter dependence
• On the rigorous foundations of the Fokas method for linear elliptic partial differential equations
• A numerical technique for linear elliptic partial differential equations in polygonal domains
• Laplace's equation on convex polyhedra via the unified method
• The Spectral Dirichlet--Neumann Map for Laplace's Equation in a Convex Polygon
• A spectrally accurate numerical implementation of the Fokas transform method for Helmholtz-type PDEs
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