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Volume 18, Issue 1
Weakly Regular Sturm-Liouville Problems: A Corrected Spectral Matrix Method

Cecilia Magherini

Int. J. Numer. Anal. Mod., 18 (2021), pp. 62-78.

Published online: 2021-02

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  • Abstract

In this paper, we consider weakly regular Sturm-Liouville eigenproblems with unbounded potential at both endpoints of the domain. We propose a Galerkin spectral matrix method for its solution and we study the error in the eigenvalue approximations it provides. The result of the convergence analysis is then used to derive a low-cost and very effective formula for the computation of corrected numerical eigenvalues. Finally, we present and discuss the results of several numerical experiments which confirm the validity of the approach.

  • Keywords

Sturm-Liouville eigenproblems, spectral matrix methods, Legendre polynomials, acceleration of convergence.

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COPYRIGHT: © Global Science Press

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@Article{IJNAM-18-62, author = {Magherini , Cecilia}, title = {Weakly Regular Sturm-Liouville Problems: A Corrected Spectral Matrix Method}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2021}, volume = {18}, number = {1}, pages = {62--78}, abstract = {

In this paper, we consider weakly regular Sturm-Liouville eigenproblems with unbounded potential at both endpoints of the domain. We propose a Galerkin spectral matrix method for its solution and we study the error in the eigenvalue approximations it provides. The result of the convergence analysis is then used to derive a low-cost and very effective formula for the computation of corrected numerical eigenvalues. Finally, we present and discuss the results of several numerical experiments which confirm the validity of the approach.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/18621.html} }
TY - JOUR T1 - Weakly Regular Sturm-Liouville Problems: A Corrected Spectral Matrix Method AU - Magherini , Cecilia JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 62 EP - 78 PY - 2021 DA - 2021/02 SN - 18 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/18621.html KW - Sturm-Liouville eigenproblems, spectral matrix methods, Legendre polynomials, acceleration of convergence. AB -

In this paper, we consider weakly regular Sturm-Liouville eigenproblems with unbounded potential at both endpoints of the domain. We propose a Galerkin spectral matrix method for its solution and we study the error in the eigenvalue approximations it provides. The result of the convergence analysis is then used to derive a low-cost and very effective formula for the computation of corrected numerical eigenvalues. Finally, we present and discuss the results of several numerical experiments which confirm the validity of the approach.

Magherini , Cecilia. (2021). Weakly Regular Sturm-Liouville Problems: A Corrected Spectral Matrix Method. International Journal of Numerical Analysis and Modeling. 18 (1). 62-78. doi:
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