Science China Mathematics

, Volume 58, Issue 11, pp 2279–2300 | Cite as

Asymptotic solvers for ordinary differential equations with multiple frequencies

  • Marissa Condon
  • Alfredo Deaño
  • Jing GaoEmail author
  • Arieh Iserles


We construct asymptotic expansions for ordinary differential equations with highly oscillatory forcing terms, focussing on the case of multiple, non-commensurate frequencies. We derive an asymptotic expansion in inverse powers of the oscillatory parameter and use its truncation as an exceedingly effective means to discretize the differential equation in question. Numerical examples illustrate the effectiveness of the method.


highly oscillatory problems ordinary differential equation modulated Fourier expansions multiple frequencies numerical analysis 


65L05 65D30 42B20 42A10 


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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Marissa Condon
    • 1
  • Alfredo Deaño
    • 2
  • Jing Gao
    • 3
    Email author
  • Arieh Iserles
    • 4
  1. 1.School of Electronic EngineeringDublin City UniversityDublin 9Ireland
  2. 2.Departmento de MatemáticasUniversidad Carlos III de MadridLeganés, MadridSpain
  3. 3.School of Mathematics and StatisticsXi’an Jiaotong UniversityXi’anChina
  4. 4.DAMTP, Centre for Mathematical SciencesUniversity of CambridgeCambridgeUK

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