An explicit Numerov-type method for second-order differential equations with oscillating solutions

In this paper a new explicit Numerov-type method is introduced. The construction is based on a modification of a sixth-order explicit Numerov-type method recently developed by Tsitouras [Ch. Tsitouras, Explicit Numerov type methods with reduced number of stages, Comput. Math. Appl. 45 (2003) 37–42]. Two free parameters are added in order to nullify the phase-lag and the amplification. The method is useful only when a good estimate of the frequency of the problem is known in advance. The parameters depend on the product of the estimated frequency and the stepsize. Numerical results obtained for well-known test problems show the efficiency of the new method.