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

  • Authors:

  • Marissa Condon;Alfredo Deaño;Jing Gao;Arieh Iserles

  • Affiliations:

  • School of Electronic Engineering, Dublin City University, Dublin, Ireland 9;Depto.de Matemáticas, Universidad Carlos III de Madrid, Legans, Spain 28911;School of Mathematics and Statistics, Xi'an Jiaotong University, Xian, China 710049;DAMTP, Centre for Mathematical Sciences, University of Cambridge, Cambridge, UK CB3 0WA

  • Venue:
  • Calcolo: a quarterly on numerical analysis and theory of computation
  • Year:
  • 2014

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Abstract

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.