A semi-analytical numerical method for solving evolution and elliptic partial differential equations

DOI10.1016/j.cam.2008.07.036zbMath1170.65079OpenAlexW2033624051MaRDI QIDQ1012495

S. A. Smitheman, Natasha Flyer, Athanassios S. Fokas, Euan A. Spence

Publication date: 21 April 2009

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

Full work available at URL: https://doi.org/10.1016/j.cam.2008.07.036

zbMATH Keywords

boundary value problemsinitial-boundary value problemselliptic partial differential equationstransform methodevolutionary partial differential equationssemi-analytical numerical methods

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Boundary value problems for second-order elliptic equations (35J25) Nonlinear boundary value problems for linear elliptic equations (35J65) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Initial value problems for second-order parabolic equations (35K15) Boundary element methods for boundary value problems involving PDEs (65N38)

Related Items (11)

Fokas transform method for a brain tumor invasion model with heterogeneous diffusion in 1+1 dimensions ⋮ Computing eigenvalues and eigenfunctions of the Laplacian for convex polygons ⋮ A Hybrid Analytical-Numerical Technique for Elliptic PDEs ⋮ Eigenvalues for the Laplace operator in the interior of an equilateral triangle ⋮ Integral representations of displacements in linear elasticity ⋮ A numerical implementation of Fokas boundary integral approach: Laplace's equation on a polygonal domain ⋮ Water waves with moving boundaries ⋮ On the Fokas method for the solution of elliptic problems in both convex and non-convex polygonal domains ⋮ The Poisson and the Biharmonic Equations in the Interior of a Convex Polygon ⋮ Construction of the differential surface admittance operator with an extended Fokas method for electromagnetic scattering at polygonal objects with arbitrary material parameters ⋮ Extended water wave systems of Boussinesq equations on a finite interval: theory and numerical analysis

Cites Work

• An analytical method for linear elliptic PDEs and its numerical implementation
• The generalized Dirichlet-Neumann map for linear elliptic PDEs and its numerical implementation
• Boundary-value problems for linear PDEs with variable coefficients
• A spectral collocation method for the Laplace and modified Helmholtz equations in a convex polygon
• From high oscillation to rapid approximation I: modified Fourier expansions
• 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
• A transform method for linear evolution PDEs on a finite interval

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