Journal of Advanced Mathematical Modeling

Journal of Advanced Mathematical Modeling

Monte Carlo Method for Solving Becker-Doring Equations with Constant Monomers

Authors
Alireza Soheili 1
Hussian Hassani 2
1 Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
2 Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran
Abstract
Stochastic differential equations (SDE) play a relevant role in many application areas such as collision, population and polymer dynamics, genetic regulation, investment  finance and biology. The procedure of
collision among particles was modeled by an infinite dimensional differential system (in the discrete case) and a nonlinear partial integro-differential equation (in the continuous case). The  discrete case may be approximated with a parabolic partial differential equation. In this paper, using the Monte-Carlo method, we obtain an approximation for solving the parabolic differential equation in the continuous form. 
Keywords
Parabolic Equation
Monte Carlo Method
Stochastic Differential Equation
Becker-Doring Equation
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(2002), Numerical method for stochastic differential equation with application, Queensland. Duncan, D.B. and Soheili, A.R. (2001), Approximating the Becker-Doring cluster equations, Appl. Numer. Math, 37, 1-29. Gusev, S.A. (2004), Monte Carlo estimates of the solution of a parabolic equation and its derivatives
made by solving stochastic differential equation, Communic. in Nonlinear Science and Numerical Simulation, 9, 177-185. Penrose, O. (1989), Metastable states for the Becker-Doring cluster equations, Comm. Math. Phys, 124, 515-541. Soheili, A.R. (2004), Continuum model of two-component Becker-Doring equations, IJMMS, 49, 2641-2648.

  • Receive Date 10 June 2013