Optimized point shifts and poles in the linear rational pseudospectral method for boundary value problems

DOI10.1016/j.jcp.2004.10.009zbMath1070.65062OpenAlexW2052826039MaRDI QIDQ1777061

Hans D. Mittelmann, Jean-Paul Berrut

Publication date: 12 May 2005

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: http://doc.rero.ch/record/4151/files/1_berrut_ops.pdf

zbMATH Keywords

convergencenumerical resultsboundary layerspseudospectral methodsMesh generationTwo-point boundary value problemsLinear rational collocationPoint shift optimizationPole optimization

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Linear boundary value problems for ordinary differential equations (34B05)

Related Items (7)

Adaptive rational spectral methods for the linear stability analysis of nonlinear fourth-order problems ⋮ Fast barycentric rational interpolations for complex functions with some singularities ⋮ A generalized eigenvalue problem for quasi-orthogonal rational functions ⋮ Linear Barycentric Rational Interpolation with Guaranteed Degree of Exactness ⋮ Barycentric rational interpolation with asymptotically monitored poles ⋮ A periodic map for linear barycentric rational trigonometric interpolation ⋮ A new map for the Chebyshev pseudospectral solution of differential equations with large gradients

Uses Software

• Matlab
• simannf90

Cites Work

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• Preconditioned minimal residual methods for Chebyshev spectral calculations
• The errors in calculating the pseudospectral differentiation matrices for Čebyšev-Gauss-Lobatto points
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• The Linear Rational Pseudospectral Method with Iteratively Optimized Poles for Two-Point Boundary Value Problems
• Minimizing multimodal functions of continuous variables with the “simulated annealing” algorithm—Corrigenda for this article is available here
• A Fast Adaptive Numerical Method for Stiff Two-Point Boundary Value Problems
• Pseudospectral Solution of Near-Singular Problems using Numerical Coordinate Transformations Based on Adaptivity
• Spectral Methods in MATLAB
• Barycentric Lagrange Interpolation
• Lagrangian Interpolation at the Chebyshev Points xn,     cos (  /n),   = 0(1)n; some Unnoted Advantages

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