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A Magnus-based integrator for Brownian parametric semi-linear oscillators

Author

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  • D'Ambrosio, Raffaele
  • de la Cruz, Hugo
  • Scalone, Carmela

Abstract

We introduce a numerical method for solving second-order stochastic differential equations of the form x¨=−ω2(t)x+f(t,x)+σ(t)ξ(t), describing a class of nonlinear oscillators with non-constant frequency, perturbed by white noise ξ(t). The proposed scheme takes advantages of the Magnus approach to construct an integrator for this stochastic oscillator. Its convergence properties are rigorously analyzed and selected numerical experiments on relevant stochastic oscillators are carried out, confirming the effectiveness and the competitive behavior of the proposed method, in comparison with standard integrators in the literature.

Suggested Citation

  • D'Ambrosio, Raffaele & de la Cruz, Hugo & Scalone, Carmela, 2024. "A Magnus-based integrator for Brownian parametric semi-linear oscillators," Applied Mathematics and Computation, Elsevier, vol. 472(C).
    • Handle: RePEc:eee:apmaco:v:472:y:2024:i:c:s0096300324000821
    DOI: 10.1016/j.amc.2024.128610
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    References listed on IDEAS

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    1. D’Ambrosio, Raffaele & Scalone, Carmela, 2021. "Two-step Runge-Kutta methods for stochastic differential equations," Applied Mathematics and Computation, Elsevier, vol. 403(C).
    2. de la Cruz, H. & Jimenez, J.C. & Biscay, R.J., 2019. "On the oscillatory behavior of coupled stochastic harmonic oscillators driven by random forces," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 85-89.
    3. Chunmei Shi & Yu Xiao & Chiping Zhang, 2012. "The Convergence and MS Stability of Exponential Euler Method for Semilinear Stochastic Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-19, September.
    4. de la Cruz, H., 2020. "Stabilized explicit methods for the approximation of stochastic systems driven by small additive noises," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
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