A numerical solution to fractional diffusion equation for force-free case

DOI10.1155/2013/187383zbMath1275.65063OpenAlexW2140447289WikidataQ58915486 ScholiaQ58915486MaRDI QIDQ369762

Orkun Tasbozan, Alaattin Esen, N. Murat Yagmurlu, Yusuf Ucar

Publication date: 19 September 2013

Published in: Abstract and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2013/187383

zbMATH Keywords

numerical examplesRiemann-Liouville operatorfractional diffusion equationcollocation finite element methodcubic B-spline functionsforce-free case

Mathematics Subject Classification ID

Heat equation (35K05) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Fractional partial differential equations (35R11)

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Cites Work

• Unnamed Item
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• Implicit finite difference approximation for time fractional diffusion equations
• Anomalous diffusion in one dimension
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• The accuracy and stability of an implicit solution method for the fractional diffusion equation
• Weighted average finite difference methods for fractional diffusion equations
• The fractional diffusion equation
• An Explicit Finite Difference Method and a New von Neumann-Type Stability Analysis for Fractional Diffusion Equations
• The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics
• The random walk's guide to anomalous diffusion: A fractional dynamics approach