Numerical analysis of time fractional three dimensional diffusion equation

Numerical analysis of time fractional three dimensional diffusion equation

The three dimensional diffusion equations were extended to the scope of fractional order derivative. The fractional operator used here is in Caputo sense. The resulting equation was solved using two numerical approaches: The forward in time and central in space method and the Crank-Nicholso...

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Main Author: Atangana Abdon
Format: Article
Language:English
Published: VINCA Institute of Nuclear Sciences 2015-01-01
Series:Thermal Science
Subjects:
three dimensional diffusion equations
fractional derivative
stability
convergence
Online Access:http://www.doiserbia.nb.rs/img/doi/0354-9836/2015/0354-983615007A .pdf
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spelling doaj-3fceff5c83a74ce3a9903aefb93f67f92021-01-02T02:29:20ZengVINCA Institute of Nuclear SciencesThermal Science0354-98362334-71632015-01-0119suppl. 171210.2298/TSCI15S10S7A0354-983615007ANumerical analysis of time fractional three dimensional diffusion equationAtangana Abdon0University of the Free State, Faculty of Natural and Agricultural Sciences, Institute for Groundwater Studies, Bloemfontein, South AfricaThe three dimensional diffusion equations were extended to the scope of fractional order derivative. The fractional operator used here is in Caputo sense. The resulting equation was solved using two numerical approaches: The forward in time and central in space method and the Crank-Nicholson method. The stability analysis of both methods was studied, and the study showed that the Crank-Nicholson method is unconditionally stable while the forward method is stable if some conditions are satisfied.http://www.doiserbia.nb.rs/img/doi/0354-9836/2015/0354-983615007A .pdfthree dimensional diffusion equationsfractional derivativestabilityconvergence
collection DOAJ
language English
format Article
sources DOAJ
author Atangana Abdon
spellingShingle Atangana Abdon
Numerical analysis of time fractional three dimensional diffusion equation
Thermal Science
three dimensional diffusion equations
fractional derivative
stability
convergence
author_facet Atangana Abdon
author_sort Atangana Abdon
title Numerical analysis of time fractional three dimensional diffusion equation
title_short Numerical analysis of time fractional three dimensional diffusion equation
title_full Numerical analysis of time fractional three dimensional diffusion equation
title_fullStr Numerical analysis of time fractional three dimensional diffusion equation
title_full_unstemmed Numerical analysis of time fractional three dimensional diffusion equation
title_sort numerical analysis of time fractional three dimensional diffusion equation
publisher VINCA Institute of Nuclear Sciences
series Thermal Science
issn 0354-9836
2334-7163
publishDate 2015-01-01
description The three dimensional diffusion equations were extended to the scope of fractional order derivative. The fractional operator used here is in Caputo sense. The resulting equation was solved using two numerical approaches: The forward in time and central in space method and the Crank-Nicholson method. The stability analysis of both methods was studied, and the study showed that the Crank-Nicholson method is unconditionally stable while the forward method is stable if some conditions are satisfied.
topic three dimensional diffusion equations
fractional derivative
stability
convergence
url http://www.doiserbia.nb.rs/img/doi/0354-9836/2015/0354-983615007A .pdf
work_keys_str_mv AT atanganaabdon numericalanalysisoftimefractionalthreedimensionaldiffusionequation
_version_ 1724361902486716416

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