Simulation of the continuous time random walk of the space-fractional diffusion equations

DOI10.1016/j.cam.2007.10.052zbMath1153.65007OpenAlexW2019457759MaRDI QIDQ955047

Rudolf Gorenflo, Entsar A. Abdel-Rehim

Publication date: 18 November 2008

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2007.10.052

zbMATH Keywords

Fokker-Planck equationnumerical examplesstochastic processesstochastic differential equationsMonte Carlo methodcontinuous time random walkspace-fractional diffusion equation\(\alpha \)-stable distributionspace-fractional derivative

Mathematics Subject Classification ID

Gaussian processes (60G15) Sums of independent random variables; random walks (60G50) Integro-partial differential equations (45K05) Fractional derivatives and integrals (26A33) Diffusion processes (60J60) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

Related Items (9)

Fundamental solutions of the fractional diffusion and the fractional Fokker-Planck equations ⋮ From the space-time fractional integral of the continuous time random walk to the space-time fractional diffusion equations, a short proof and simulation ⋮ Implicit difference scheme of the space-time fractional advection diffusion equation ⋮ A spectral Legendre-Gauss-Lobatto collocation method for a space-fractional advection diffusion equations with variable coefficients ⋮ On partially inexact HSS iteration methods for the complex symmetric linear systems in space fractional CNLS equations ⋮ Anomalous diffusion modeling by fractal and fractional derivatives ⋮ The need for the fractional operators ⋮ A new numerical algorithm for solving a class of fractional advection-dispersion equation with variable coefficients using Jacobi polynomials ⋮ From power laws to fractional diffusion processes with and without external forces, the non direct way

Cites Work

• From power laws to fractional diffusion: the direct way
• Random walks with infinite spatial and temporal moments
• The Fokker-Planck equation. Methods of solution and applications.
• Fractional Fokker–Planck equation for nonlinear stochastic differential equations driven by non-Gaussian Lévy stable noises
• Random Walks on Lattices. II
• The fundamental solution of the space-time fractional diffusion equation
• Random walk models approximating symmetric space-fractional diffusion processes
• Fractional kinetic equations: solutions and applications
• Chance and Stability
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