Mapped barycentric Chebyshev differentiation matrix method for the solution of regular Sturm-Liouville problems

DOI10.1016/j.amc.2010.07.027zbMath1202.65101OpenAlexW2091037557MaRDI QIDQ606764

Xuecang Zhang

Publication date: 18 November 2010

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

Full work available at URL: https://doi.org/10.1016/j.amc.2010.07.027

zbMATH Keywords

eigenvaluenumerical examplesSturm-Liouville problemsspectral methodconformal mapChebyshev collocation methodmatrix eigenvalue problemsbarycentric rational interpolationspectral differentiation matrix

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical differentiation (65D25) Numerical approximation of eigenvalues and of other parts of the spectrum of ordinary differential operators (34L16) Numerical solution of eigenvalue problems involving ordinary differential equations (65L15)

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Chebyshev differentiation matrices for efficient computation of the eigenvalues of fourth-order Sturm-Liouville problems ⋮ An efficient numerical technique for estimating eigenvalues of second-order non-self-adjoint Sturm-Liouville problems ⋮ Marching schemes for Cauchy wave propagation problems in laterally varying waveguides ⋮ Finite difference methods for half inverse Sturm-Liouville problems ⋮ A simple approach for determining the eigenvalues of the fourth-order Sturm-Liouville problem with variable coefficients ⋮ Inverse Sturm–Liouville problems with pseudospectral methods ⋮ Fast and accurate calculations of fourth-order non-self-adjoint Sturm-Liouville eigenvalues for problems in physics and engineering ⋮ On using Bernstein scheme for computation of the eigenvalues of fourth-order Sturm-Liouville problems

Uses Software

• Matlab
• MATSLISE
• chebop
• Differentiation Matrix Suite

Cites Work

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• Efficient computation of high index Sturm-Liouville eigenvalues for problems in physics
• Approximate calculation of eigenvalues with the method of weighted residuals-collocation method
• The chebop system for automatic solution of differential equations
• Correction of finite element estimates for Sturm-Liouville eigenvalues
• Sturm-Liouville operators and applications. Transl. from the Russian by A. Iacob
• Mappings and accuracy for Chebyshev pseudo-spectral approximations
• A modified Chebyshev pseudospectral method with an \(O(N^{-1})\) time step restriction
• Asymptotic correction of more Sturm-Liouville eigenvalue estimates.
• Spectral methods for incompressible viscous flow
• Floquet theory for left-definite Sturm-Liouville problems
• Asymptotic correction of Numerov's eigenvalue estimates with natural boundary conditions
• Approximation properties of a mapped Chebyshev method
• Improving the accuracy of the matrix differentiation method for arbitrary collocation points
• Approximate solution of the Sturm-Liouville problems with Legendre-Galerkin-Chebyshev collocation method
• An improvement for Chebyshev collocation method in solving certain Sturm-Liouville problems
• Approximations of Sturm-Liouville eigenvalues using differential quadrature (DQ) method
• Spectral methods on arbitrary grids
• Approximate solution of periodic Sturm-Liouville problems with Chebyshev collocation method
• Approximate computation of eigenvalues with Chebyshev collocation method
• MATSLISE
• The Eigenvalues of Second-Order Spectral Differentiation Matrices
• Correction of finite difference eigenvalues of periodic Sturm-Liouville problems
• Exponential convergence of a linear rational interpolant between transformed Chebyshev points
• Accuracy Enhancement for Higher Derivatives using Chebyshev Collocation and a Mapping Technique
• Spectral Methods in MATLAB
• Barycentric Lagrange Interpolation
• Accuracy, Resolution, and Stability Properties of a Modified Chebyshev Method
• A Practical Guide to Pseudospectral Methods
• Complex WKB analysis of a -symmetric eigenvalue problem
• Rational Chebyshev spectral methods for unbounded solutions on an infinite interval using polynomial-growth special basis functions

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