A preconditioned implementation of pseudospectral methods on arbitrary grids.

DOI10.1016/S0096-3003(02)00823-8zbMath1053.65058MaRDI QIDQ1415259

Farideh Ghoreishi, Mohammed Hosseini Ali Abadi

Publication date: 3 December 2003

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

zbMATH Keywords

pseudospectral methodnumerical examplesboundary value problemscondition numberpreconditionereigenvalue spectrumarbitrary grid

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) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Numerical computation of matrix norms, conditioning, scaling (65F35) Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60)

Related Items (7)

The adaptive operational tau method for systems of ODEs ⋮ Multidomain pseudospectral integration preconditioning matrices for the advection and the diffusion operators ⋮ Fractional pseudospectral integration matrices for solving fractional differential, integral, and integro-differential equations ⋮ Fast, accurate, and small-scale direct trajectory optimization using a Gegenbauer transcription method ⋮ From stepwise integrations and low-rank updates to a pseudospectral solution operator matrix for the Helmholtz operator \(\frac{d}{dx} a(x) \frac{d}{dx} + c(x)\) ⋮ Integration matrix based on arbitrary grids with a preconditioner for pseudospectral method ⋮ Inverse matrices for pseudospectral differentiation operators in polar coordinates by stepwise integrations and low-rank updates

Cites Work

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• Chebyshev pseudospectral solution of second-order elliptic equations with finite element preconditioning
• Spectral methods for problems in complex geometries
• A fast algorithm for spectral differentiation
• Multipole expansions and pseudospectral cardinal functions: A new generalization of the fast Fourier transform
• A modified Chebyshev pseudospectral method with an \(O(N^{-1})\) time step restriction
• Spectral methods on arbitrary grids
• A Preconditioning Matrix for the Chebyshev Differencing Operator
• Integration Preconditioning of Pseudospectral Operators. I. Basic Linear Operators
• Accuracy Enhancement for Higher Derivatives using Chebyshev Collocation and a Mapping Technique

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