Numerical Solution to Anomalous Diffusion Equations for Levy Walks

Abstract

The process of Levy random walks is considered in view of the constant velocity of a particle. A kinetic equation is obtained that describes the process of walks, and fractional differential equations are obtained that describe the asymptotic behavior of the process. It is shown that, in the case of finite and infinite mathematical expectation of paths, these equations have a completely different form. To solve the obtained equations, the method of local estimation of the Monte Carlo method is described. The solution algorithm is described and the advantages and disadvantages of the considered method are indicated.

Keywords

• Levy walks
• anomalous diffusion
• fractional material derivative
• combustion process
• local estimate
• Monte Carlo method