Stochastic solution for Cauchy one-dimensional advection model in mean square calculus

This work is concerned with the discussion of the numerical approximation for random Cauchy transport model in one dimension. The random (forward time, backward space) finite difference scheme is used to find the stochastic solution. The impression of the consistency and the random von-Neumann stability technique under the mean square sense are studied. Using some examples, we can support our main objective of this model statistically.