Abstract

We present a new approach to the numerical solution of Sturm-Liouville eigenvalue problems based on Magnus expansions. Our algorithms are closely related to Pruess' methods [Pre73], but provide for high order approximations at nearly the same cost as the second-order Pruess method. By using Newton iteration to solve for the eigenvalues, we are able to present an efficient algorithm for computing a range of eigenvalues and eigenfunctions. Numerical experiments display promising results, and asymptotic corrections are made to improve further the accuracy of the schemes.

Citations

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