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 - <p style="text-align: justify;">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.</p>