Runge-Kutta methods for quadratic ordinary differential equations

被引：11
|
作者：
Iserles, A
Ramaswami, G
Sofroniou, M
机构：
[1] Univ Cambridge, Dept Appl Math & Theoret Phys, Cambridge CB3 9EW, England
[2] Univ Valladolid, Dept Matemat Aplicada & Computac, E-47005 Valladolid, Spain
[3] Wolfram Res Inc, Champaign, IL 61820 USA
来源：
BIT NUMERICAL MATHEMATICS | 1998年 / 38卷 / 02期
关键词：
Runge-Kutta methods; quadratic odes; binary trees;
D O I：
10.1007/BF02512370
中图分类号：
TP31 [计算机软件];
学科分类号：
081202 ; 0835 ;
摘要：
Many systems of ordinary differential equations are quadratic: the derivative can be expressed as a quadratic function of the dependent variable. We demonstrate that this feature can be exploited in the numerical solution by Runge-Kutta methods, since the quadratic structure serves to decrease the number of order conditions. We discuss issues related to construction design and implementation and present a number of new methods of Runge-Kutta and Runge-Kutta-Nystrom type that display superior behaviour when applied to quadratic ordinary differential equations.
引用
收藏
页码：315 / 346
页数：32
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