A Galerkin spectral matrix method is proposed for weakly regular Sturm-Liouville eigenproblems with singular potentials, along with a convergence-based correction formula for eigenvalues validated by numerical experiments.
Sidi, Asymptotic expansion of Legendre series coefficients fo r functions with endpoint singularities, Asymptotic Analysis 65 (2009) 175-190
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Weakly regular Sturm-Liouville problems: a corrected spectral matrix method
A Galerkin spectral matrix method is proposed for weakly regular Sturm-Liouville eigenproblems with singular potentials, along with a convergence-based correction formula for eigenvalues validated by numerical experiments.