Phohomsiri, Phailaung; Udwadia, Firdaus E. Acceleration of Runge-Kutta integration schemes. (English) Zbl 1067.65070 Discrete Dyn. Nat. Soc. 2004, No. 2, 307-314 (2004). Summary: 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. Cited in 3 Documents MSC: 65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations 65L05 Numerical methods for initial value problems involving ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems 65Y20 Complexity and performance of numerical algorithms Keywords:numerical examples; Runge-Kutta scheme; computational efficiency PDFBibTeX XMLCite \textit{P. Phohomsiri} and \textit{F. E. Udwadia}, Discrete Dyn. Nat. Soc. 2004, No. 2, 307--314 (2004; Zbl 1067.65070) Full Text: DOI EuDML