An Extended Pruess Method for Sturm-Liouville Problems
Robert Carlson
TL;DR
This paper introduces an enhanced Pruess method that uses specialized potential approximations with elementary solutions to more accurately compute eigenvalues in Sturm-Liouville problems.
Contribution
The paper develops a novel version of the Pruess method employing translates of 2/cos^2(x) for improved eigenvalue calculations in Sturm-Liouville problems.
Findings
Enhanced accuracy in eigenvalue computation.
Efficient approximation with elementary solutions.
Applicable to a broader class of Sturm-Liouville problems.
Abstract
A new version of the piecewise approximation (Pruess) method is developed for calculating eigenvalues of Sturm-Liouville problems. The usual piecewise constant or piecewise linear potential approximations are replaced by translates of , whose corresponding eigenvalue equation has elementary solutions.
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Taxonomy
TopicsScientific Research and Discoveries · Quantum chaos and dynamical systems · Spectral Theory in Mathematical Physics