Spectral corrections for Sturm-Liouville problems

DOI10.1016/S0377-0427(00)00446-5zbMath0988.65057MaRDI QIDQ5946116

Marco Marlettta, G. Gheri, Paolo Ghelardoni

Publication date: 14 July 2002

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

zbMATH Keywords

numerical exampleserror boundseigenfunctionsshooting methodsNewton iterationsspectral correctionsSturm-Liouville eigenvalue problems

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) Error bounds for numerical methods for ordinary differential equations (65L70) 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) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15)

Related Items (8)

Boundary value method for inverse Sturm-Liouville problems ⋮ Numerical solution of vector Sturm-Liouville problems with Dirichlet conditions and nonlinear dependence on the spectral parameter ⋮ Solving Sturm-Liouville inverse problems by an orthogonalized enhanced boundary function method and a product formula for symmetric potential ⋮ Computing the eigenvalues of the generalized Sturm-Liouville problems based on the Lie-group \(SL(2,\mathbb R)\) ⋮ A quasi-extrapolation procedure for error estimation of numerical methods in Sturm--Liouville eigenproblems. ⋮ The synthesis of an inhomogeneous elastic system with a boundary load ⋮ Improvement of eigenvalues of Sturm-Liouville problem with \(t\)-periodic boundary conditions ⋮ A polynomial approach to the spectral corrections for Sturm-Liouville problems

Uses Software

• SLCPM12

Cites Work

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• Correction of finite element eigenvalues for problems with natural or periodic boundary conditions
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• A parallel approach to the modified Numerov-like eigenvalue determination for Sturm-Liouville problems
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• CP methods for the Schrödinger equation revisited
• SLCPM12 -- a program for solving regular Sturm-Liouville problems
• Error estimates for parallel shooting using initial or boundary value methods
• Parallel shooting with error estimate for increasing the accuracy
• A modified numerov method for higher sturm-liouville eigenvalues
• Correction of finite difference eigenvalues of periodic Sturm-Liouville problems
• Accurate computation of higher Sturm-Liouville eigenvalues

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