TITLE:
Two Implicit Runge-Kutta Methods for Stochastic Differential Equation
AUTHORS:
Fuwen Lu, Zhiyong Wang
KEYWORDS:
Stochastic Differential Equation; Implicit Stochastic Runge-Kutta Method; Order Condition
JOURNAL NAME:
Applied Mathematics,
Vol.3 No.10,
October
12,
2012
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.