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

We study a numerical method for second-order differential equations in whic h high-frequency oscillations are generated by a linear part. For example, semilinear wave equations are of this type. The numerical scheme is based o n the requirement that it solves linear problems with constant inhomogeneit y exactly. We prove that the method admits second-order error bounds which are independent of the product of the step size with the frequencies. Our a nalysis also provides new insight into the mollified impulse method of Garc ia-Archilla, Sanz-Serna, and Skeel. We include results of numerical experim ents with the sine-Cordon equation. Mathematics Subject Classification (199 1): 65L05, 65L70, 65M12, 65M20.