Non-standard finite difference and Chebyshev collocation methods for solving fractional diffusion equation

In this paper, a new numerical technique for solving the fractional order diffusion equation is introduced. This technique basically depends on the Non-Standard finite difference method (NSFD) and Chebyshev collocation method, where the fractional derivatives are described in terms of the Caputo sen...

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Bibliographic Details
Published in:Physica A 2018-06, Vol.500, p.40-49
Main Authors: Agarwal, P., El-Sayed, A.A.
Format: Article
Language:English
Subjects:
Caputo derivative
Chebyshev collocation method
Non-standard finite difference method
The fractional diffusion equation
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Summary:In this paper, a new numerical technique for solving the fractional order diffusion equation is introduced. This technique basically depends on the Non-Standard finite difference method (NSFD) and Chebyshev collocation method, where the fractional derivatives are described in terms of the Caputo sense. The Chebyshev collocation method with the (NSFD) method is used to convert the problem into a system of algebraic equations. These equations solved numerically using Newton’s iteration method. The applicability, reliability, and efficiency of the presented technique are demonstrated through some given numerical examples.
ISSN:0378-4371
1873-2119
DOI:10.1016/j.physa.2018.02.014