Implicit difference scheme of the space-time fractional advection diffusion equation

DOI10.1515/fca-2015-0084zbMath1336.65128OpenAlexW2567124937MaRDI QIDQ898906

Entsar A. Abdel-Rehim

Publication date: 21 December 2015

Published in: Fractional Calculus \& Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/fca-2015-0084

zbMATH Keywords

theta-methodnumerical resultGrünwald-Letnikov schemeimplicit difference schemesCaputo time-fractional derivativeinverse Riesz potentialLax-Richtmer and von-Neumann stabilityspace-time fractional advection-diffusion equationstransport at the Earth surface

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Fractional partial differential equations (35R11)

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Cites Work

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• From the Ehrenfest model to time-fractional stochastic processes
• Approximation of the Lévy-Feller advection-dispersion process by random walk and finite difference method
• Convergence of the Grünwald-Letnikov scheme for time-fractional diffusion
• Simulation of the continuous time random walk of the space-fractional diffusion equations
• Conservative difference schemes for diffusion problems with boundary and interface conditions
• The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• Approximation of Lévy-Feller diffusion by random walk
• Time fractional diffusion: A discrete random walk approach
• Finite difference approximations for fractional advection-dispersion flow equations
• Approximate solutions for the fractional advection-dispersion equation using Legendre pseudo-spectral method
• Survey of the stability of linear finite difference equations
• Numerical solutions of the space-time fractional advection-dispersion equation
• Fractional kinetic equations: solutions and applications
• Fractional Calculus: Integral and Differential Equations of Fractional Order
• Random Walk and the Theory of Brownian Motion