On asymptotic expansion solvers for highly oscillatory semi-explicit DAEs

Marissa Condon; Jing  Gao; Arieh Iserles

doi:10.3934/dcds.2016008

Article Contents

2016, Volume 36, Issue 9: 4813-4837. Doi: 10.3934/dcds.2016008

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On asymptotic expansion solvers for highly oscillatory semi-explicit DAEs

1.
School of Electronic Engineering, Dublin City University, Dublin 9
2.
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, Shaanxi
3.
Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Rd, Cambridge CB3 0WA

Received: January 31, 2014

Revised: February 29, 2016

Published: May 2017

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Abstract

The paper is concerned with the discretization and solution of DAEs of index $1$ and subject to a highly oscillatory forcing term. Separate asymptotic expansions in inverse powers of the oscillatory parameter are constructed to approximate the differential and algebraic variables of the DAEs. The series are truncated to enable practical implementation. Numerical experiments are provided to illustrate the effectiveness of the method.

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Mathematics Subject Classification: Primary: 65L80, 34E05; Secondary: 34A09.

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