On error bounds for the Gautschi-type exponential integrator applied to oscillatory second-order differential equations

Authors:
Volker Grimm
Affiliations:
La Trobe University, Mathematics Department, Bundoora, 3086, Melbourne, VIC, Australia
Venue:
Numerische Mathematik
Year:
2005

Citing 0
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Abstract

This paper studies a numerical method for second-order oscillatory differential equations in which high-frequency oscillations are generated by a linear time- and/or solution-dependent part. For constant linear part, it is known that the method allows second-order error bounds independent of the product of the step-size with the frequencies and is therefore a long-time-step method. Most real-world problems are not of that kind and it is important to study more general equations. The analysis in this paper shows that one obtains second-order error bounds even in the case of a time- and/or solution-dependent linear part if the matrix is evaluated at averaged positions.