Some Modified Runge-Kutta Methods for the Numerical Solution of Initial-Value Problems with Oscillating Solutions

@article{Simos1998SomeMR,
title={Some Modified Runge-Kutta Methods for the Numerical Solution of Initial-Value Problems with Oscillating Solutions},
author={Theodore E. Simos},
journal={J. Sci. Comput.},
year={1998},
volume={13},
pages={51-63}
}

Two new modified Runge-Kutta methods with minimal phase-lag are developed for the numerical solution of initial-value problems with oscillating solutions which can be analyzed to a system of first order ordinary differential equations. These methods are based on the well known Runge-Kutta RK5(4)7FEql method of Higham and Hall (1990) of order five. Also, based on the property of the phase-lag a new error control procedure is introduced. Numerical and theoretical results show that this newâ€¦Â CONTINUE READING