Solving Oscillatory Problems Using an Optimized Runge–Kutta Method

New explicit Runge–Kutta method with zero phase-lag, zero first derivative of the phase-lag and zero amplification error is derived for the effective numerical integration of second-order initial-value problems with oscillatory solutions in this paper. The new method is based on the sixth-stage fifth-order Runge–Kutta method. Numerical illustrations show that the new proposed method is much efficient as compared with other Runge–Kutta methods in the scientific literature, for the numerical integration of oscillatory problems.