Rosenbrock-Type Methods for Solving Stochastic Differential Equations

IF 0.4 Q4 MATHEMATICS, APPLIED

Numerical Analysis and Applications Pub Date : 2024-05-28 DOI:10.1134/s1995423924020010

T. A. Averina, K. A. Rybakov

引用次数: 0

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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求解随机微分方程的罗森布洛克式方法

摘要本文回顾了最近发表的有关随机微分方程（SDE）数学模型及其在各个领域应用的文章。本文旨在简要介绍用于近似求解 SDE 的 Rosenbrock 型方法。它说明了如何在不增加太多实现复杂性的情况下，改善数值方法的性能并提高计算精度。论文还针对具有乘法非交换噪声的 SDE 提出了一种新的 Rosenbrock 型方法。通过建立旋转扩散模型对该方法进行了测试。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Numerical Analysis and Applications MATHEMATICS, APPLIED-

CiteScore

1.00

自引率

0.00%

发文量

期刊介绍： Numerical Analysis and Applications is the translation of Russian periodical Sibirskii Zhurnal Vychislitel’noi Matematiki (Siberian Journal of Numerical Mathematics) published by the Siberian Branch of the Russian Academy of Sciences Publishing House since 1998. The aim of this journal is to demonstrate, in concentrated form, to the Russian and International Mathematical Community the latest and most important investigations of Siberian numerical mathematicians in various scientific and engineering fields. The journal deals with the following topics: Theory and practice of computational methods, mathematical physics, and other applied fields; Mathematical models of elasticity theory, hydrodynamics, gas dynamics, and geophysics; Parallelizing of algorithms; Models and methods of bioinformatics.