Discrete Dynamics in Nature and Society 
Volume 2004 (2004), Issue 2, Pages 307-314
doi:10.1155/S1026022604311039

Acceleration of Runge-Kutta integration schemes

Phailaung Phohomsiri1 and Firdaus E. Udwadia2

 1Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles 90089-1453, CA, USA
2Departments of Civil Engineering, Aerospace and Mechanical Engineering, Mathematics, and Operations and Information Management, University of Southern California, Los Angeles 90089, CA, USA
Received 24 November 2003

Abstract

A simple accelerated third-order Runge-Kutta-type, fixed time step, integration scheme that uses just two function evaluations per step is developed. Because of the lower number of function evaluations, the scheme proposed herein has a lower computational cost than the standard third-order Runge-Kutta scheme while maintaining the same order of local accuracy. Numerical examples illustrating the computational efficiency and accuracy are presented and the actual speedup when the accelerated algorithm is implemented is also provided.