Numerical approximations for fractional diffusion equations via a Chebyshev spectral-tau method

• Authors: Eid Doha , Ali Bhrawy , Samer Ezz-Eldien
• Languages of publication: EN

Abstracts

EN

In this paper, a class of fractional diffusion equations with variable coefficients is considered. An accurate and efficient spectral tau technique for solving the fractional diffusion equations numerically is proposed. This method is based upon Chebyshev tau approximation together with Chebyshev operational matrix of Caputo fractional differentiation. Such approach has the advantage of reducing the problem to the solution of a system of algebraic equations, which may then be solved by any standard numerical technique. We apply this general method to solve four specific examples. In each of the examples considered, the numerical results show that the proposed method is of high accuracy and is efficient for solving the time-dependent fractional diffusion equations.

Keywords

EN

fractional diffusion equations; spectral tau technique; operational matrix; shifted Chebyshev polynomials

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2013
• Volume: 11
• Issue: 10
• Pages: 1494-1503

Dates

published

1 - 10 - 2013

online

19 - 12 - 2013

Contributors

author

Eid Doha

• Department of Mathematics, Faculty of Science, Cairo University, Giza, 12613, Egypt

author

Ali Bhrawy

author

Samer Ezz-Eldien

• Department of Basic Science, Institute of Information Technology, Modern Academy, Cairo, 11931, Egypt

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Identifiers

DOI

10.2478/s11534-013-0264-7