Asymptotic solvers for second-order differential equation systems with multiple frequencies
In this paper, an asymptotic expansion is constructed to solve second-order differential 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 effective method of dicretizing the differential equation system in question. Numerical experiments illustrate the effectiveness of the asymptotic method in contrast to the standard RungeKutta method.
second-order differential equations multiple frequencies highly oscillatory problems modulated fourier expansions numerical analysis 65l05 65d30 42b20 42a10