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arXiv · 2608.16396

A weak order 2 Runge-Kutta method for It\^o stochastic delay differential equations

Alessia andò·Dimitri Breda·Faraz William
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Abstract

We present a Runge-Kutta method of weak order 2 for the numerical time integration of stochastic delay differential equations. This scheme extends the class of second order Runge-Kutta methods introduced by A. R\"o{\ss}ler in [SIAM J. Numer. Anal., 47(3):1713-1738, 2009] for stochastic ordinary differential equations. The proposed integrator is applicable to equations with discrete commensurable delays and is particularly efficient for problems involving multiple noise terms. Experimental confirmation of the weak order 2 is provided and MATLAB codes are freely available.

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Alessia andò, Dimitri Breda, Faraz William. 2026-08-17. A weak order 2 Runge-Kutta method for It\^o stochastic delay differential equations. https://arxiv.org/abs/2608.16396

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