Asymptotic solvers for second-order differential equation systems with multiple frequencies
DEAÑO CABRERA, ALFREDO
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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 Runge-Kutta method. © 2013 Springer-Verlag Italia.
highly oscillatory problems; modulated fourier expansions; multiple frequencies; numerical analysis; second-order differential equations