Open Access

ARTICLE

The Fourth-Order Group Preserving Methods for the Integrations of Ordinary Differential Equations

by Hung-Chang Lee¹, Chein-Shan Liu²

1 Department of Mechanical Engineering, Kun Shan University, Tainan, Taiwan
2 Department of Civil Engineering, National Taiwan University, Taipei, Taiwan. E-mail: liuchei.nshan@msa.hinet.net

Computer Modeling in Engineering & Sciences 2009, 41(1), 1-26. https://doi.org/10.3970/cmes.2009.041.001

Abstract

The group-preserving schemes developed by Liu (2001) for integrating ordinary differential equations system were adopted the Cayley transform and Padé approximants to formulate the Lie group from its Lie algebra. However, the accuracy of those schemes is not better than second-order. In order to increase the accuracy by employing the group-preserving schemes on ordinary differential equations, according to an efficient technique developed by Runge and Kutta to raise the order of accuracy from the Euler method, we combine the Runge-Kutta method on the group-preserving schemes to obtain the higher-order numerical methods of group-preserving type. They provide single-step explicit time integrators for differential equations. Several numerical examples are examined, showing that the higher-order group-preserving schemes have good computational efficiency and high accuracy.

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Keywords

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