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IMA Journal of Numerical Analysis Advance Access originally published online on June 10, 2008
IMA Journal of Numerical Analysis 2009 29(3):595-605; doi:10.1093/imanum/drn031
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© The author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Modulated Fourier expansions and heterogeneous multiscale methods

J. M. Sanz-Serna{dagger}

Departamento de Matemática Aplicada, Universidad de Valladolid, Spain

{dagger} Email: sanzsern{at}mac.uva.es

Received on 20 December 2007. Revised on 8 April 2008.


  Abstract

We show that, for highly oscillatory ordinary differential equation problems, the modulated Fourier expansion approach can be advantageously used to understand and analyse the heterogeneous multiscale methods introduced by E, Engquist and their co-workers.

Key Words: modulated Fourier expansions; heterogeneous multiscale methods; highly oscillatory differential equations; inverted pendulum

Dedicated to Arieh Iserles on his 60th birthday


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