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

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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.

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Authors and Affiliations

  1. Mathematics Department, La Trobe University, Bundoora, Melbourne, VIC, 3086, Australia

    Volker Grimm

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  1. Volker Grimm
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Correspondence to Volker Grimm.

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Mathematics Subject Classification (2000): 65L05, 65L70

Acknowledgement I am grateful to Marlis Hochbruck and Christian Lubich for helpful discussions on the subject.

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Grimm, V. On error bounds for the Gautschi-type exponential integrator applied to oscillatory second-order differential equations. Numer. Math. 100, 71–89 (2005). https://doi.org/10.1007/s00211-005-0583-8

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  • DOI: https://doi.org/10.1007/s00211-005-0583-8

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