Two Implicit Runge-Kutta Methods for Stochastic Differential Equation

Fuwen Lu, Zhiyong Wang

Department of Mathematics, University of electronic Science and Technology of China, Chengdu Sichuan, China.

DOI: 10.4236/am.2012.310162                

Abstract

In this paper, the Ito-Taylor expansion of stochastic differential equation is briefly introduced. The colored rooted tree theory is applied to derive strong order 1.0 implicit stochastic Runge-Kutta method(SRK). Two fully implicit schemes are presented and their stability qualities are discussed. And the numerical report illustrates the better numerical behavior.

Keywords

Stochastic Differential Equation; Implicit Stochastic Runge-Kutta Method; Order Condition

Conflicts of Interest

The authors declare no conflicts of interest.

References

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