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Burrage, P.M. (1999) Runge-Kutta Methods for Stochastic Differential Equations. Ph.D. Thesis, University of Queensland, Queensland, Australia.

has been cited by the following article:

• TITLE: Stability of Stochastic Logistic Model with Ornstein-Uhlenbeck Process for Cell Growth of Microorganism in Fermentation Process

  AUTHORS: Tawfiqullah Ayoubi

  KEYWORDS: Stability, Fermentation Process, Ornstein-Uhlenbeck Process, Logistic Model, Lyapunov Function, 4-Stage Stochastic Runge-Kutta Method

  JOURNAL NAME: Applied Mathematics, Vol.10 No.8, August 13, 2019

  ABSTRACT: Current research is concerned with the stability of stochastic logistic equation with Ornstein-Uhlenbeck process. First, this research proves that the stochastic logistic model with Ornstein-Uhlenbeck process has a positive solution. After that, it also introduces the sufficient conditions for stochastically stability of stochastic logistic model for cell growth of microorganism in fermentation process for positive equilibrium point by using Lyapunov function. In addition, this research establishes the sufficient conditions for zero solution as mentioned in Appendix A due to the cell growth of microorganism μmax, which cannot be negative in fermentation process. Furthermore, for numerical simulation, current research uses the 4-stage stochastic Runge-Kutta (SRK4) method to show the reality of the results.