کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4645124 | 1632187 | 2014 | 21 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On numerical methods for nonlinear singularly perturbed Schrödinger problems
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات محاسباتی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
In this article, we develop a new method to compute positive mountain pass solutions, which improves the results for a large range of singular parameters. We extend ideas from MPA considering the singulary perturbed problems by developing a finite element approach mixed with steepest descend directions. We use a modified line search method based on Armijo's rule for improving the Newton search and Patankar trick for preserving the positiveness of the solution. To improve the range of the singular parameter, adaptive methods based on Dual Weighted Residual method are used. Our numerical experiments are performed with the deal.II library and we show that it is possible to get solutions for ε=10â6 improving the current results in four orders of magnitude. At this level, machine precision must be considered for further studies.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Numerical Mathematics - Volume 86, December 2014, Pages 22-42
Journal: Applied Numerical Mathematics - Volume 86, December 2014, Pages 22-42
نویسندگان
A.I. Ávila, A. Meister, M. Steigemann,