TY - JOUR

T1 - Rosenbrock-Type Methods for Solving Stochastic Differential Equations

AU - Averina, T. A.

AU - Rybakov, K. A.

PY - 2024/6

Y1 - 2024/6

N2 - 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.

AB - 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.

KW - Euler–Maruyama method

KW - Milstein method

KW - Rosenbrock-type method

KW - numerical method

KW - rotational diffusion

KW - stochastic differential equations

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85195139205&origin=inward&txGid=62bc1035dd72ac9c183cfd7c205d04b5

UR - https://www.mendeley.com/catalogue/6628a833-01b6-36ef-8b8a-dbba1a8ddd26/

U2 - 10.1134/S1995423924020010

DO - 10.1134/S1995423924020010

M3 - Article

VL - 17

SP - 99

EP - 115

JO - Numerical Analysis and Applications

JF - Numerical Analysis and Applications

SN - 1995-4239

IS - 2

ER -