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arXiv · 2607.15300

Theory and Computation of Discrete Sturm--Liouville Problems on Non-Uniform Grids via the Pr\"ufer Transformation

Bailyn Hall·Kimsear Lor
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Abstract

We study a discrete version of the Sturm--Liouville eigenvalue problem on grids whose spacing may vary from point to point, using the discrete Pr\"ufer transformation. We show that any eigenvalues of the problem are real and that there are finitely many of them. We then compare two numerical methods for computing the eigenvalues, regular shooting and Pr\"ufer-based shooting, and find that the Pr\"ufer method remains accurate on non-uniform grids where regular shooting loses accuracy or fails.

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Bailyn Hall, Kimsear Lor. 2026-07-09. Theory and Computation of Discrete Sturm--Liouville Problems on Non-Uniform Grids via the Pr\"ufer Transformation. https://arxiv.org/abs/2607.15300

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