A numerical comparison of Chebyshev methods for solving fourth order semilinear initial boundary value problems

DOI10.1016/j.cam.2009.12.029zbMath1188.65140OpenAlexW2109921465MaRDI QIDQ964956

Benson K. Muite

Publication date: 21 April 2010

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.2009.12.029

zbMATH Keywords

numerical examplespreconditioningChebyshev spectral methodChebyshev tau methodChebyshev collocation methodfast methodstime steppinglinear fourth order boundary value problemssemilinear initial boundary value problems

Mathematics Subject Classification ID

Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Linear boundary value problems for ordinary differential equations (34B05) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50) Preconditioners for iterative methods (65F08) Higher-order semilinear hyperbolic equations (35L76)

Related Items (12)

Pseudospectral versus Galerkin methods: fourth order equations ⋮ Tensor calculus in polar coordinates using Jacobi polynomials ⋮ Tensor calculus in spherical coordinates using Jacobi polynomials. I: Mathematical analysis and derivations ⋮ Confinement of rotating convection by a laterally varying magnetic field ⋮ New space-time spectral and structured spectral element methods for high order problems ⋮ Spectral integration of linear boundary value problems ⋮ A new collocation scheme using non-polynomial basis functions ⋮ An effective Chebyshev tau meshless domain decomposition method based on the integration-differentiation for solving fourth order equations ⋮ Polar differentiation matrices for the Laplace equation in the disk under nonhomogeneous Dirichlet, Neumann and Robin boundary conditions and the biharmonic equation under nonhomogeneous Dirichlet conditions ⋮ On Green's function-based time stepping for semilinear initial-boundary value problems ⋮ Chebyshev tau meshless method based on the integration-differentiation for biharmonic-type equations on irregular domain ⋮ The chebop system for automatic solution of differential equations

Uses Software

• Matlab
• mctoolbox
• Eigtool
• CSparse

Cites Work

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