Rosenbrock-type methods for solving stochastic differential equations
T.A. Averina1,2, K.A. Rybakov3
1Institute of Computational Mathematics and Mathematical Geophysics of Siberian Branch of Russian Academy of Sciences, Novosibirsk, Russia
2Novosibirsk State University, Novosibirsk, Russia
3Moscow Aviation Institute (National Research University), Moscow, Russia
Keywords: stochastic differential equations, Euler-Maruyama method, Milstein method, Rosenbrock-type method, numerical method, rotational diffusion
Abstract
This paper reviews recent publications that describe mathematical models with stochastic differential equations (SDEs) and applications in various fields. The purpose of this paper is to briefly describe Rosenbrock-type methods for approximate solution of SDEs. It shows how the performance of the numerical methods can be improved and the accuracy of calculations can be increased without increasing the implementation complexity too much. The paper also proposes a new Rosenbrock-type method for SDEs with multiplicative non-commutative noise. Its testing is carried out by modeling rotational diffusion.
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