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Asymptotic solvers for ordinary differential equations with multiple frequencies

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Abstract

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.

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Authors and Affiliations

  1. School of Electronic Engineering, Dublin City University, Dublin 9, Ireland

    Marissa Condon

  2. Departmento de Matemáticas, Universidad Carlos III de Madrid, Leganés, Madrid, CP-28911, Spain

    Alfredo Deaño

  3. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, China

    Jing Gao

  4. DAMTP, Centre for Mathematical Sciences, University of Cambridge, Cambridge, CB3 0WA, UK

    Arieh Iserles

Authors
  1. Marissa Condon
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  2. Alfredo Deaño
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  3. Jing Gao
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  4. Arieh Iserles
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Corresponding author

Correspondence to Jing Gao.

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Condon, M., Deaño, A., Gao, J. et al. Asymptotic solvers for ordinary differential equations with multiple frequencies. Sci. China Math. 58, 2279–2300 (2015). https://doi.org/10.1007/s11425-015-5066-5

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  • DOI: https://doi.org/10.1007/s11425-015-5066-5

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