2019/07/12 by Cecilia Magherini, Magherini, Cecilia
Computer Science · Mathematics · #65B99 #65L15 #65L60 #65L70 #FOS: Mathematics #Numerical Analysis (math.NA) #cs.NA #math.NA #msc:65B99 #msc:65L15 #msc:65L60 #msc:65L70
paper · pdf · doi:10.48550/arxiv.1907.07615
arXiv admin note: text overlap with arXiv:1812.02090
arxiv created 2019/07/12 · arxiv updated 2019/07/18
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.