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


1 Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran

2 Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran


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. 


مراجع Ball, J.M., Carr, J. and Penrose, O. (1986), The Becker-Doring equations, Basic properties and asymptotic behaviour of solutions, Comm. Math. Phys, 104, 657-692. Burrage, K. and Burrage, P.M.
(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.