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On the numerical discretisation of stochastic oscillators

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  • Cohen, David

Abstract

In this article, we propose an approach, based on the variation-of-constants formula, for the numerical discretisation over long-time intervals of several stochastic oscillators. Additive and multiplicative noises are treated separately. The proposed schemes permit the use of large step sizes in the presence of a high frequency in the problem and offer various additional properties. These new numerical integrators can be viewed as a stochastic-generalisation of the trigonometric integrators for highly oscillatory deterministic problems.

Suggested Citation

  • Cohen, David, 2012. "On the numerical discretisation of stochastic oscillators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(8), pages 1478-1495.
    • Handle: RePEc:eee:matcom:v:82:y:2012:i:8:p:1478-1495
    DOI: 10.1016/j.matcom.2012.02.004
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    Cited by:

    1. Carmela Scalone, 2022. "A Numerical Scheme for Harmonic Stochastic Oscillators Based on Asymptotic Expansions," Mathematics, MDPI, vol. 10(17), pages 1-9, August.
    2. Tocino, A. & Komori, Y. & Mitsui, T., 2022. "Integration of the stochastic underdamped harmonic oscillator by the θ-method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 199(C), pages 217-230.

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