Abstract
Eigenvalue problems with eigenparameter appearing in the boundary conditions usually have complicated characteristic determinant where zeros cannot be explicitly computed. In this paper, we use the derivative sampling theorem “Hermite interpolations” to compute approximate values of the eigenvalues of Sturm-Liouville problems with eigenvalue parameter in one or two boundary conditions. We use recently derived estimates for the truncation and amplitude errors to compute error bounds. Also, using computable error bounds, we obtain eigenvalue enclosures. Also numerical examples, which are given at the end of the paper, give comparisons with the classical sinc method and explain that the Hermite interpolations method gives remarkably better results.
Highlights
The mathematical modeling of many practical problems in mechanics and other areas of mathematical physics requires solutions of boundary value problems and fractional differential equations
Eigenvalue problems with eigenparameter appearing in the boundary conditions usually have complicated characteristic determinant where zeros cannot be explicitly computed
Numerical examples, which are given at the end of the paper, give comparisons with the classical sinc method and explain that the Hermite interpolations method gives remarkably better results
Summary
Approximation of Eigenvalues of Sturm-Liouville Problems by Using Hermite Interpolation. Eigenvalue problems with eigenparameter appearing in the boundary conditions usually have complicated characteristic determinant where zeros cannot be explicitly computed. We use the derivative sampling theorem “Hermite interpolations” to compute approximate values of the eigenvalues of Sturm-Liouville problems with eigenvalue parameter in one or two boundary conditions. We use recently derived estimates for the truncation and amplitude errors to compute error bounds. Using computable error bounds, we obtain eigenvalue enclosures. Numerical examples, which are given at the end of the paper, give comparisons with the classical sinc method and explain that the Hermite interpolations method gives remarkably better results
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