Discrete Dynamics in Nature and Society
Volume 2004 (2004), Issue 2, Pages 307-314
Acceleration of Runge-Kutta integration schemes
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
Copyright © 2004 Phailaung Phohomsiri and Firdaus E. Udwadia. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.