Abstract
Any random model represents an action where uncertainty is present. In this article, we investigate a random process solution of the random convection–diffusion model using the finite difference technique. Additionally, the consistency and stability of the random difference scheme is studied under mean square and mean fourth calculus using the direct expectation way. The effect of the randomness input is discussed in order to obtain a stochastic process solution by applying mean square and mean fourth calculus. Some case studies for different statistical distributions are stable under our conditions.
Highlights
The purpose of this work is to provide the finite difference scheme from an applied point of view
Much more emphasis is put into solution methods rather than to analysis of the theoretical properties of the equations; in this paper we will try to apply the mean square and mean fourth calculus in order to find the stability condition for the random process solution of the following random problem:
Solute transport from a source through a random medium of air or water is characterized by a parabolic stochastic partial differential equation derived on the principle of conservation of mass; it is known as stochastic advection–diffusion equation (SADE)
Summary
The purpose of this work is to provide the finite difference scheme from an applied point of view. Much more emphasis is put into solution methods rather than to analysis of the theoretical properties of the equations; in this paper we will try to apply the mean square and mean fourth calculus in order to find the stability condition for the random process solution of the following random problem:. Many papers have studied stochastic partial differential equations by using the Brownian motion process [1,2,3] with a random potential [3]. 3, we prove that our difference scheme is consistent in mean square and mean fourth with the advection–diffusion model, in Sect. 4, we will find the stability condition in mean square and mean fourth for the random difference scheme.
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