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A Numerical Scheme for Harmonic Stochastic Oscillators Based on Asymptotic Expansions

Author

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  • Carmela Scalone

    (Department of Engineering and Computer Science and Mathematics, University of L’Aquila, 67100 L’Aquila, Italy)

Abstract

In this work, we provide a numerical method for discretizing linear stochastic oscillators with high constant frequencies driven by a nonlinear time-varying force and a random force. The presented method is constructed by starting from the variation of constants formula, in which highly oscillating integrals appear. To provide a suited discretisation of this type of integrals, we propose quadrature rules based on asymptotic expansions. Theoretical considerations and numerical experiments comparing the method with a standard approach on physical models are introduced.

Suggested Citation

  • Carmela Scalone, 2022. "A Numerical Scheme for Harmonic Stochastic Oscillators Based on Asymptotic Expansions," Mathematics, MDPI, vol. 10(17), pages 1-9, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:17:p:3083-:d:899288
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    References listed on IDEAS

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    1. Cohen, David, 2012. "On the numerical discretisation of stochastic oscillators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(8), pages 1478-1495.
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