随机微分方程的平衡隐式两步丸山方法

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-12-12 DOI:10.1016/j.cnsns.2024.108512

Quanwei Ren, Jiayi Liu, Yanyan He

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Balanced implicit two-step Maruyama methods for stochastic differential equations

This paper introduces balanced implicit two-step Maruyama methods for solving Itô stochastic differential equations. Such methods, compared to those corresponding standard linear two-step Maruyama methods, have better mean-square properties, which is confirmed by a comparison of the stability regions for some particular two-step Maruyama methods. Moreover, the convergence order is investigated which proves the convergence of the presented methods with the order 12 in the mean-square sense. Numerical results are reported to show the convergence properties and the stability properties of the balanced implicit two-step Maruyama methods. The stability analysis and numerical results show that the proposed methods are very promising methods for stiff stochastic differential equations.

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.