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...
Main Author: | |
---|---|
Format: | Article |
Language: | English |
Published: |
VINCA Institute of Nuclear Sciences
2015-01-01
|
Series: | Thermal Science |
Subjects: | |
Online Access: | http://www.doiserbia.nb.rs/img/doi/0354-9836/2015/0354-983615007A .pdf |
id |
doaj-3fceff5c83a74ce3a9903aefb93f67f9 |
---|---|
record_format |
Article |
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 |