Symbolic derivation of Runge-Kutta-Nyström type order conditions and methods for solving

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• 作者：Ioannis Th. Famelis ; ^a ; ^{ifamelis@teiath.gr} ; ; Ch. Tsitouras^b ;
• 关键词：Enumeration of trees ; Symbolic generation of trees ; Order conditions ; Differential evolution
• 刊名：Applied Mathematics and Computation
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：297
• 期：Complete
• 页码：50-60
• 全文大小：1227 K
• 卷排序：297

文摘

In this work we study the Runge–Kutta–Nyström (RKN) type methods for the solution of a special third order initial value problems. Based on rooted trees the relative order conditions theory is presented introducing a new set of SN-trees named ⊤_{3 whose elements’ enumeration is given. A Mathematica package, that furnishes instantly order conditions of high orders, is also listed. Finally, a new method of order 8 is constructed that outperforms by far the methods found in the literature.}