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 Phomomsiri1
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
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.