Construction and mean-square stability analysis of a new family of stochastic Runge-Kutta methods

被引：1

作者：

Rahimi, Vaz'he ^{[1
]}

Ahmadian, Davood ^{[1
]}

Ballestra, Luca Vincenzo ^{[2
,3
]}

机构：

[1] Univ Tabriz, Fac Math Stat & Comp Sci, Dept Appl Math, 29 Bahman Blvd, Tabriz, Iran

[2] Alma Mater Studiorum Univ Bologna, Via Belle Arti 41, I-40126 Bologna, Italy

[3] INDAM GNCS Res Grp, Bologna, Italy

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2024年 / 470卷

关键词：

Second-order; Stochastic Runge-Kutta method; Mean-square stability; Butcher table; WEAK APPROXIMATION; ORDER CONDITIONS; SCHEMES;

D O I：

10.1016/j.amc.2024.128570

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This research paper investigates the convergence and stability of two diagonal drift -implicit second -order stochastic Runge-Kutta methods for weak approximation of systems containing three-dimensional drift and noise terms in Ito stochastic differential equations. The first method is based on the approach presented by Debrabant and Rossler (2008) [5], while the second method utilizes a Butcher table that, to the best of our knowledge, has not been used in previous research. We compare the convergence and stability of both methods and analyze their respective stability regions. The results show that the method using the newly introduced Butcher table is not only reliable but also highly efficient.

引用

页数：11

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