Weak second order S-ROCK methods for Stratonovich stochastic differential equations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:236

Article

Komori, Yoshio¹  Burrage, Kevin^2,3 

[1] Kyushu Inst Technol, Dept Syst Design & Informat, Iizuka, Fukuoka 8208502, Japan

[2] Univ Oxford, Dept Comp Sci, Oxford OX1 3QD, England

[3] Queensland Univ Technol, Discipline Math, Brisbane, Qld 4001, Australia

关键词: Explicit method;    Mean square stability;    Stochastic orthogonal Runge-Kutta Chebyshey method;   

DOI  :  10.1016/j.cam.2012.01.033

来源: Elsevier

【 摘 要 】

It is well known that the numerical solution of stiff stochastic ordinary differential equations leads to a step size reduction when explicit methods are used. 'this has led to a plethora of implicit or semi-implicit methods with a wide variety of stability properties. However, for stiff stochastic problems in which the eigenvalues of a drift term lie near the negative real axis, such as those arising from stochastic partial differential equations, explicit methods with extended stability regions can be very effective. In the present paper our aim is to derive explicit Runge-Kutta schemes for non-commutative Stratonovich stochastic differential equations, which are of weak order two and which have large stability regions. This will be achieved by the use of a technique in Chebyshev methods for ordinary differential equations. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free