A Gautschi-type method for oscillatory second-order differential equations

We study a numerical method for second-order differential equations in which high-frequency oscillations are generated by a linear part. For example, semilinear wave equations are of this type. The numerical scheme is based on the requirement that it solves linear problems with constant inhomogeneity exactly. We prove that the method admits secondorder error bounds which are independent of the product of the step size with the frequencies. Our analysis also provides new insight into the mollified impulse method of Garcı́a-Archilla, Sanz-Serna, and Skeel. We include results of numerical experiments with the sine-Gordon equation.