Chebyshev differentiation matrices for efficient computation of the eigenvalues of fourth-order Sturm-Liouville problems

DOI10.1016/j.apm.2012.09.062zbMath1426.65109OpenAlexW1996129076MaRDI QIDQ1667745

Peng Zhang

Publication date: 30 August 2018

Published in: Applied Mathematical Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apm.2012.09.062

zbMATH Keywords

eigenvaluesspectral-collocation methodChebyshev differentiation matrixfourth-order Sturm-Liouville problems

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of eigenvalue problems involving ordinary differential equations (65L15) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15)

Related Items (10)

An efficient method to approximate eigenvalues and eigenfunctions of high order Sturm-Liouville problems ⋮ An efficient numerical technique for estimating eigenvalues of second-order non-self-adjoint Sturm-Liouville problems ⋮ Theory and numerical approaches of high order fractional Sturm–Liouville problems ⋮ Existence of solutions for a sixth-order nonlinear equation ⋮ An efficient technique for finding the eigenvalues and the eigenelements of fourth-order Sturm-Liouville problems ⋮ Solution of eigenvalue problems for linear Hamiltonian systems with a nonlinear dependence on the spectral parameter ⋮ Computing high-index eigenvalues of singular Sturm-Liouville problems ⋮ Numerical approximations of Sturm–Liouville eigenvalues using Chebyshev polynomial expansions method ⋮ 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
• SLEUTH
• SLEDGE
• Differentiation Matrix Suite

Cites Work

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• Differential quadrature method (DQM) and Boubaker polynomials expansion scheme (BPES) for efficient computation of the eigenvalues of fourth-order Sturm-Liouville problems
• Approximate solution of periodic Sturm-Liouville problems with Chebyshev collocation method
• Approximate computation of eigenvalues with Chebyshev collocation method
• A spectral element approach for the stability of delay systems
• An Oscillation Method for Fourth-Order, Selfadjoint, Two-Point Boundary Value Problems with Nonlinear Eigenvalues
• Automatic Solution of the Sturm-Liouville Problem
• Algorithm 775
• Convergence Analysis of Spectral Collocation Methods for a Singular Differential Equation
• Spectral Methods in MATLAB
• Accuracy, Resolution, and Stability Properties of a Modified Chebyshev Method
• Oscillation theory and numerical solution of fourth-order Sturm—Liouville problems
• Pseudospectral collocation methods for fourth-order differential equations
• Spectral Methods

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