Chebyshev tau matrix method for Poisson-type equations in irregular domain

DOI10.1016/j.cam.2008.09.011zbMath1165.65081OpenAlexW2032929684MaRDI QIDQ1019781

Weibin Kong, Xiong-Hua Wu

Publication date: 28 May 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.2008.09.011

zbMATH Keywords

numerical experimentsPoisson-type equationirregular domainnonlinear problemsvariable coefficientsmeshless methodHelmholtz problemsChebyshev tau matrix method

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Boundary value problems for second-order elliptic equations (35J25) Nonlinear boundary value problems for linear elliptic equations (35J65) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (15)

Error analysis of the Chebyshev collocation method for linear second-order partial differential equations ⋮ Improving the accuracy of Chebyshev Tau method for nonlinear differential problems ⋮ The numerical solution of the nonlinear Klein-Gordon and sine-Gordon equations using the Chebyshev tau meshless method ⋮ Haar wavelets method for solving Poisson equations with jump conditions in irregular domain ⋮ Chebyshev tau meshless method based on the highest derivative for fourth order equations ⋮ Application of Chebyshev tau method for bending analysis of elastically restrained edge functionally graded nano/micro-scaled sandwich beams, under non-uniform normal and shear loads ⋮ A direct Chebyshev collocation method for the numerical solutions of three-dimensional Helmholtz-type equations ⋮ Geometrically transformed spectral methods to solve partial differential equations in circular geometries, application for multi-phase flow ⋮ Novel approach to spectral methods for irregular domains ⋮ The Poisson problem: a comparison between two approaches based on SPH method ⋮ Bernstein series solution of linear second-order partial differential equations with mixed conditions ⋮ An effective Chebyshev tau meshless domain decomposition method based on the integration-differentiation for solving fourth order equations ⋮ Explicit formulae for integro-differential operational matrices ⋮ Chebyshev tau meshless method based on the integration-differentiation for biharmonic-type equations on irregular domain ⋮ A high-order embedded domain method combining a predictor-corrector-Fourier-continuation-Gram method with an integral Fourier pseudospectral collocation method for solving linear partial differential equations in complex domains

Cites Work

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• Differential quadrature Trefftz method for Poisson-type problems on irregular domains
• Domain imbedding methods for the Stokes equations
• A spectral embedding method applied to the advection-diffusion equation
• A meshless method for generalized linear or nonlinear Poisson-type problems
• Spectral Integration and Two-Point Boundary Value Problems
• Solving multivariable mathematical models by the quadrature and cubature methods
• Differential quadrature domain decomposition method for problems on a triangular domain
• Spectral Methods
• Trigonometric Interpolation of Empirical and Analytical Functions

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