Explicit pseudo-symplectic Runge-Kutta methods for stochastic Hamiltonian systems

被引：1

作者：

Anton, Cristina ^{[1
]}

机构：

[1] Grant MacEwan Univ, Dept Math & Stat, 5-103C,10700 104 Ave NW, Edmonton, AB T5J 4S2, Canada

来源：

APPLIED NUMERICAL MATHEMATICS | 2023年 / 185卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

Stochastic Hamiltonian systems; Stochastic Runge-Kutta methods; Quadratic invariants; Symplectic integration; Pseudo-symplectic method; ORDER CONDITIONS; QUADRATIC-INVARIANTS; SYMPLECTIC SCHEMES; APPROXIMATION;

D O I：

10.1016/j.apnum.2022.11.013

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give conditions for stochastic Runge-Kutta methods to near preserve quadratic invari-ants, and we discuss the associated simplified order conditions. For stochastic Hamiltonian systems we propose a systematic approach to construct explicit stochastic Runge-Kutta pseudo-symplectic schemes. Our approach is based on colored trees and B-series. We con-struct some pseudo-symplectic stochastic Runge-Kutta methods with strong convergence order, and we illustrate numerically the long term performance of the proposed schemes. (c) 2022 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：18 / 37

页数：20

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