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Two-step Runge-Kutta methods for stochastic differential equations

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  • D’Ambrosio, Raffaele
  • Scalone, Carmela

Abstract

We introduce a theory of two-step Runge-Kutta (TSRK) methods for stochastic differential equations, arising from the perturbation of the corresponding TSRK methods for deterministic problems. We present a proof of convergence and study the mean-square stability properties. Numerical experiments confirming the theoretical results are provided.

Suggested Citation

  • D’Ambrosio, Raffaele & Scalone, Carmela, 2021. "Two-step Runge-Kutta methods for stochastic differential equations," Applied Mathematics and Computation, Elsevier, vol. 403(C).
    • Handle: RePEc:eee:apmaco:v:403:y:2021:i:c:s0096300320308833
    DOI: 10.1016/j.amc.2020.125930
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    References listed on IDEAS

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    1. Ren, Quanwei & Tian, Hongjiong, 2018. "Generalized two-step Maruyama methods for stochastic differential equations," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 48-57.
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    Cited by:

    1. 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).

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