کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
10349549 | 863660 | 2014 | 10 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A simplified Nyström-tree theory for extended Runge-Kutta-Nyström integrators solving multi-frequency oscillatory systems
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
شیمی
شیمی تئوریک و عملی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
In the study of extended Runge-Kutta-Nyström (abbr. ERKN) methods for the integration of multi-frequency oscillatory systems, a quite complicated set of algebraic conditions arises which must be satisfied for a method to achieve some specified order. A theory of tri-colored tree was proposed by Yang et al. (2009), for achieving the order conditions of ERKN methods which are designed specially for multi-frequency and multidimensional perturbed oscillators. The tri-colored tree theory for the order conditions in that paper is useful, but not completely satisfactory due to the existence of redundant trees. In this paper, a simplified tri-colored theory and the order conditions for ERKN integrators are developed by constructing a set of simplified special extended Nyström trees (abbr. SSENT) and defining some real-valued mappings on it. In order to simplify the tri-colored tree theory, two special mappings, the extended elementary differential and the sign mapping for a tree are investigated in detail. This leads to a novel Nyström-tree theory for the order conditions for ERKN methods without any redundant trees, which simplifies the tri-colored theory.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computer Physics Communications - Volume 185, Issue 11, November 2014, Pages 2841-2850
Journal: Computer Physics Communications - Volume 185, Issue 11, November 2014, Pages 2841-2850
نویسندگان
Hongli Yang, Xianyang Zeng, Xinyuan Wu, Zhengliang Ru,