An explicit hybrid method of Numerov type for second-order periodic initial-value problems

We consider a two-parameter family of explicit hybrid methods of Numerov type for the numerical integration of second-order intial-value problems. When these methods are applied to the linear equation: y″ + ω2y = 0, ω > 0, we determine the parameters α, β so that the phase lag (frequency distortion) of the method is minimal. The resulting method has (algebraic) order 4 and a small frequency distortion of size (13628800)v8 (v = ωh, h being the step size) and in addition it possesses an interval of periodicity of size 4.63, which is larger than the interval of periodicity corresponding to the explicit method of Chawla and Rao (1986). The application of this method to equations describing free and weakly forced oscillations reveals its superiority over other methods.