## Efficient approximation of Sturm-Liouville problems using Lie-group methods (1998)

Citations: | 15 - 0 self |

### BibTeX

@MISC{Moan98efficientapproximation,

author = {Per Christian Moan},

title = {Efficient approximation of Sturm-Liouville problems using Lie-group methods},

year = {1998}

}

### Years of Citing Articles

### OpenURL

### 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.