An accurate numerical technique for solving two-dimensional time fractional order diffusion equation. (3rd July 2019)

• Record Type: Journal Article
• Authors: Nagy, A. M.; El-Sayed, Adel A.
• Is Part Of: International journal of modelling & simulation. Volume 39:Number 3(2019)
• Page Start: 214
• Page End: 221
• Publication Date: 2019-07-03
• Subjects: Two-dimensional time fractional diffusion equation -- chebyshev polynomials of the first kind -- Sinc function -- Caputo fractional derivative; Mathematical models -- Periodicals; Simulation methods -- Periodicals; Mathematical models; Simulation methods; Periodicals; 003.3
• DOI: 10.1080/02286203.2019.1592285
• Languages: English
• ISSNs: 0228-6203

Abstract

ABSTRACT: In this paper, we consider a numerical technique for solving the two-dimensional fractional order diffusion equation with a time fractional derivative. The proposed technique depends basically on the fact that an expansion of the required approximate solution in a series of shifted Chebyshev polynomials of the first kind in the time and the Sinc function in the space. Then, the expansion coefficients are determined by reducing the problem with the initial conditions to a system of algebraic equations. The fractional derivatives are expressed in the Caputo sense. The numerical results of the proposed technique are compared with other published results to show the efficiency of the presented technique.