کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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502178 | 863687 | 2009 | 10 صفحه PDF | دانلود رایگان |

Finding the eigenvalues of a Sturm–Liouville problem can be a computationally challenging task, especially when a large set of eigenvalues is computed, or just when particularly large eigenvalues are sought. This is a consequence of the highly oscillatory behavior of the solutions corresponding to high eigenvalues, which forces a naive integrator to take increasingly smaller steps. We will discuss the most used approaches to the numerical solution of the Sturm–Liouville problem: finite differences and variational methods, both leading to a matrix eigenvalue problem; shooting methods using an initial-value solver; and coefficient approximation methods. Special attention will be paid to techniques that yield uniform approximation over the whole eigenvalue spectrum and that allow large steps even for high eigenvalues.
Journal: Computer Physics Communications - Volume 180, Issue 2, February 2009, Pages 241–250