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The computation of negative eigenvalues of singular Sturm–Liouville problems
Amin Boumenir,B. Chanane +1 more
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In this article, a new interpolation method for the computation of eigenvalues of singular Sturm-Liouville problems was developed, where basic properties of the Jost solutions were used to determine the growth of the boundary function.Abstract:
In this work we shall develop a new interpolation method for the computation of eigenvalues of singular Sturm-Liouville problems. Basic properties of the Jost solutions are used to determine the growth of the boundary function and an appropriate interpolation basis. This leads to a good approximation of the negative eigenvalues.read more
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Journal ArticleDOI
Computation of the eigenvalues of Sturm-Liouville problems with parameter dependent boundary conditions using the regularized sampling method
TL;DR: The purpose in this paper is to compute the eigenvalues of Sturm-Liouville problems with quite general separated boundary conditions nonlinear in the eigenevalue parameter using the regularized sampling method, an improvement on the method based on Shannon sampling theory, which does not involve any multiple integration and provides higher order estimates of the Eigenvalues at a very low cost.
Journal ArticleDOI
Sampling Eigenvalues in Hardy Spaces
Amin Boumenir,Vu Kim Tuan +1 more
TL;DR: The sampling method is extended to compute eigenvalues of singular non-self-adjoint Sturm-Liouville problems in the presence of a continuous spectrum and a new sampling formula is developed for its reconstruction.
Journal ArticleDOI
Computing the eigenvalues of singular Sturm–Liouville problems using the regularized sampling method
TL;DR: The domain of application of the regularized sampling method is extended, a method to compute the eigenvalues, and a few numerical examples will be presented to illustrate the merit of the method.
Journal ArticleDOI
The computation of eigenvalues of singular Sturm--Liouville operators
Amin Boumenir,Vu Kim Tuan +1 more
TL;DR: A key feature of the method that leads to a fast algorithm is to combine generating functions with the Laplace transform to compute explicitly the entries of the matrix without numerical integration.
Journal ArticleDOI
Representation and sampling of Hardy functions
Amin Boumenir,Vu Kim Tuan +1 more
TL;DR: In this paper, a new sampling formula and a new series representation of the Riemann zeta function in the half plane are presented. But they do not consider the truncation error.