Author(s)

Fuwen Lu, Zhiyong Wang

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

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.

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

F. Lu and Z. Wang, "Two Implicit Runge-Kutta Methods for Stochastic Differential Equation," Applied Mathematics, Vol. 3 No. 10, 2012, pp. 1103-1108. doi: 10.4236/am.2012.310162.