PHASE FITTED CLASSICAL RUNGE-KUTTA METHOD OF ORDER FOUR FOR SOLVING OSCILLATORY PROBLEMS

In this paper, we derive a new phase fitted Runge-Kutta method based on the existing classical Runge-Kutta method of order four to solve ordinary differential equations with oscillatory solutions. The new method has the property of zero phase-lag and zero dissipation. Phase-lag or dispersion error is the angle between the true and the approximated solution, whereas dissipation is the distance of the computed solution from the standard cyclic solution. A set of problems are tested upon over a large interval and the numerical results proved that the method is more accurate compared to the classical fourth order Runge-Kutta method.