Numerical Solution to Anomalous Diffusion Equations for Levy Walks

Viacheslav V. Saenko, Vladislav N. Kovalnogov, Ruslan V. Fedorov and Yuri E. Chamchiyan
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Viacheslav V. Saenko: Laboratory for Interdisciplinary Problems of Energy Reproduction, Ulyanovsk State Technical University, 32, Severny Venets St., 432027 Ulyanovsk, Russia
Vladislav N. Kovalnogov: Laboratory for Interdisciplinary Problems of Energy Reproduction, Ulyanovsk State Technical University, 32, Severny Venets St., 432027 Ulyanovsk, Russia
Ruslan V. Fedorov: Laboratory for Interdisciplinary Problems of Energy Reproduction, Ulyanovsk State Technical University, 32, Severny Venets St., 432027 Ulyanovsk, Russia
Yuri E. Chamchiyan: Laboratory for Interdisciplinary Problems of Energy Reproduction, Ulyanovsk State Technical University, 32, Severny Venets St., 432027 Ulyanovsk, Russia

Mathematics, 2021, vol. 9, issue 24, 1-17

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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