Weakly regular Sturm-Liouville problems: a corrected spectral matrix method

2019/07/12 by Magherini, Cecilia
#65B99 #65L15 #65L60 #65L70 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1907.07615

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.

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