کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
502178 863687 2009 10 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Efficient computation of high index Sturm–Liouville eigenvalues for problems in physics
موضوعات مرتبط
مهندسی و علوم پایه شیمی شیمی تئوریک و عملی
پیش نمایش صفحه اول مقاله
Efficient computation of high index Sturm–Liouville eigenvalues for problems in physics
چکیده انگلیسی

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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computer Physics Communications - Volume 180, Issue 2, February 2009, Pages 241–250
نویسندگان
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