Solving second-order telegraph equations with high-frequency extrinsic oscillations

Abstract

We present an asymptotic method to compute efficiently second-order telegraph equations with high-frequency extrinsic oscillations. This method is based on asymptotic expansions in inverse powers of the oscillatory parameter. Each term of this asymptotic expansion is the sum of at most two coefficients. Each coefficient is derived either by recursion or by solving a non-oscillatory problem. This leads to method which exhibit improved performance with growing frequency of oscillation.