THERMAL SCIENCE

International Scientific Journal

Ali H. Bhrawy

,

Dumitru Baleanu

,

Fouad Othman M. Mallawi

A NEW NUMERICAL TECHNIQUE FOR SOLVING FRACTIONAL SUB-DIFFUSION AND REACTION SUB-DIFFUSION EQUATIONS WITH A NON-LINEAR SOURCE TERM

ABSTRACT
In this paper, we are concerned with the fractional sub-diffusion equation with a non-linear source term. The Legendre spectral collocation method is introduced together with the operational matrix of fractional derivatives (described in the Caputo sense) to solve the fractional sub-diffusion equation with a non-linear source term. The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations which greatly simplifying the problem. In addition, the Legendre spectral collocation methods applied also for a solution of the fractional reaction sub-diffusion equation with a non-linear source term. For confirming the validity and accuracy of the numerical scheme proposed, two numerical examples with their approximate solutions are presented with comparisons between our numerical results and those obtained by other methods.
KEYWORDS
local fractional variational iteration method, diffusion equation, non-differentiable solution, local fractional derivative
PAPER SUBMITTED: 2014-11-26
PAPER REVISED: 2015-01-10
PAPER ACCEPTED: 2015-02-15
PUBLISHED ONLINE: 2015-08-02
DOI REFERENCE: https://doi.org/10.2298/TSCI15S1S25B
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2015, VOLUME 19, ISSUE Supplement 1, PAGES [S25 - S34]
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A new numerical technique for solving fractional sub-diffusion and reaction sub-diffusion equations with a non-linear source term

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