Random difference scheme for diffusion advection model

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.