Phase-fitted partitioned Runge-Kutta methods for separable oscillatory Hamiltonian systems and related problems

We present an approach for deriving some phase-fitted Parti tioned Runge-Kutta (PRK) methods for numerical integration of separable Hamiltonian and related systems. The approach constitute the modification of the existing PRK such that some parameters are modified to eliminate the phase-lag and the amplification error using the analysis of phase properties. The new coefficients are derived such that an estimate of the frequency of the problem is adapted to the new coefficient such that oscillatory properties of the system is effectively handled by the modified schemes. Numerical results obtained for well-known test problems show the efficiency of the new method.