This article is cited in 5 papers

Rosenbrock-type methods for solving stochastic differential equations

T. A. Averina^ab, K. A. Rybakov<sup>c

a</sup> Institute of Computational Mathematics and Mathematical Geophysics of Siberian Branch of Russian Academy of Sciences, Russia
^b Novosibirsk State University, Russia
^c Moscow Aviation Institute (National Research University), Moscow, Russia

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.

Key words: stochastic differential equations, Euler-Maruyama method, Milstein method, Rosenbrock-type method, numerical method, rotational diffusion.

UDC: 519.676

Received: 04.01.2024
Revised: 28.02.2024
Accepted: 04.03.2024

DOI: 10.15372/SJNM20240201

 English version: Numerical Analysis and Applications, 2024, 17:2, 99–115