Hybrid Runge–Kutta methods for ordinary differential equations

被引：0

作者：

Zhongli Liu

Jintao Hu

Hongjiong Tian

机构：

[1] Shanghai University of International Business and Economics,School of Statistics and Information

[2] Shanghai Normal University,Department of Mathematics

来源：

Computational and Applied Mathematics | 2020年 / 39卷

关键词：

Hybrid Runge–Kutta method; Order conditions; Stability; A-stability; L-stability; 65L05; 65L06;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We propose a class of s-stage hybrid Runge–Kutta methods for solving ordinary differential equations and study their order conditions and numerical stability property. Examples of second-, third-, and fifth-order hybrid Runge–Kutta methods are given. Numerical experiments are conducted to demonstrate the efficiency of the proposed methods.

引用

共 6 条

[1] Burrage K(1978)A special family of Runge–Kutta methods for solving stiff differential equations BIT 18 22-41
[2] Butcher JC(1964)Implicit Runge–Kutta process Math Comp 18 50-64
[3] Chartier P(1994)L-stable parallel one-block methods for ordinary differential equations SIAM J Numer Anal 31 552-571
[4] Franco JM(1997)SDIRK methods for stiff ODEs with oscillating solutions J Comput Appl Math 81 197-209
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