Stochastic Heat and Advection CauchySohalya MA*, Yassena MT and Elbaza IM
Faculty of Science, Department of Mathematics, Mansoura University, Egypt
- *Corresponding Author:
- Sohalya MA
Faculty of Science, Department of Mathematics
Mansoura University, Egypt
Tel: +20 50 2383781
E-mail: [email protected]; [email protected]; [email protected]
Received date: January 28, 2017; Accepted date: March 14, 2017; Published date: March 21, 2017
Citation: Sohalya MA, Yassena MT, Elbaza IM (2017) Stochastic Heat and Advection Cauchy. J Appl Computat Math 6:345. doi: 10.4172/2168-9679.1000345
Copyright: © 2017 Sohalya MA, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
In this paper, the solutions of Cauchy problems for the stochastic advection and stochastic diffusion equations are obtained using the finite difference method. In the case when the flow velocity is a function of stochastic flow velocity and also, the diffusion coefficient in the stochastic heat equation is a function of stochastic diffusion coefficient, the consistency and stability of the finite difference scheme we are used need to be performed under mean square calculus.