Phailaung Phohomsiri, Firdaus E. Udwadia, "Acceleration of Runge-Kutta integration schemes", Discrete Dynamics in Nature and Society, vol. 2004, Article ID 430475, 8 pages, 2004. https://doi.org/10.1155/S1026022604311039
Acceleration of Runge-Kutta integration schemes
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.
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