Asymptotic solvers for second-order differential equation systems with multiple frequencies

Abstract

In this paper, an asymptotic expansion is constructed to solve second-order dierential equation systems with highly oscillatory forcing terms involving multiple frequencies. An asymptotic expansion is derived in inverse of powers of the oscillatory parameter and its truncation results in a very eective method of dicretizing the dierential equation system in question. Numerical experiments illustrate the eectiveness of the asymptotic method in contrast to the standard Runge-Kutta method