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T. H. Tian, “Implicit Numerical Methods for Stiff Stochastic Differential Equations and Numerical Simulations of Stochasic Models,” Ph.D. Thesis, The University of Queensland, Queensland, 2001.

has been cited by the following article:

• 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.