Runge-Kutta interpolants with minimal phase-lag

Abstract

We develop the basic theory for the construction of explicit Scaled Runge-Kutta methods (SRK) for the integration of first order differential equations having an oscillatory solution. Based on this theory and on the theory of Runge-Kutta methods with minimal phase-lag, we construct an embedded Runge-Kutta 10(12) method and an explicit scaled Runge-Kutta method. Numerical results indicate the efficiency of the new algorithms.