Runge-Kutta methods for quadratic ordinary differential equations

被引：0
|
作者：
Arieh Iserles
Geetha Ramaswami
Mark Sofroniou
机构：
[1] University of Cambridge,Department of Applied Mathematics and Theoretical Physics
[2] Universidad de Valladolid,Departamento de Matemática Aplicada y Computación
[3] Wolfram Research Inc.,Department of Mathematics
[4] Indian Institute of Science,undefined
来源：
BIT Numerical Mathematics | 1998年 / 38卷
关键词：
65L06; Runge-Kutta methods; quadratic odes; binary trees;
D O I：
暂无
中图分类号：
学科分类号：
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-Nyström type that display superior behaviour when applied to quadratic ordinary differential equations.
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页码：315 / 346
页数：31
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