Finite-difference schemes for a diffusion equation with fractional derivatives in a multidimensional domain

DOI10.1134/S001226611307001XzbMath1286.65094OpenAlexW2036793979WikidataQ115252028 ScholiaQ115252028MaRDI QIDQ2435150

I. A. Timoshchenko, N. G. Abrashina-Zhadaeva

Publication date: 3 February 2014

Published in: Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s001226611307001x

zbMATH Keywords

stabilitydiffusion equationfinite differencefractional derivativemultidimensional domain

Mathematics Subject Classification ID

Heat equation (35K05) 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)

Related Items (5)

A finite-difference scheme on a graded mesh for solving Cauchy problems with a fractional Caputo derivative in a Banach space ⋮ Discrete approximation of solutions of the Cauchy problem for a linear homogeneous differential-operator equation with a Caputo fractional derivative in a Banach space ⋮ Difference schemes for partial differential equations of fractional order ⋮ On the stability and convergence of difference schemes for the generalized fractional diffusion equation with Robin boundary value conditions ⋮ On the convergence of difference schemes for fractional differential equations with Robin boundary conditions

Cites Work

• Anomalous diffusion of particles with a finite free-motion velocity
• On using random walks to solve the space-fractional advection-dispersion equations
• Finite difference approximations for two-sided space-fractional partial differential equations
• Locally one-dimensional difference schemes for the fractional order diffusion equation
• The fundamental solution of the space-time fractional diffusion equation
• The random walk's guide to anomalous diffusion: A fractional dynamics approach
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