An efficient numerical approach for solving the variable-order time fractional diffusion equation using chebyshev spectral collocation method

Document Type : Research Paper

Authors

1 DEPARTMENT OF MATHEMATICS, BEHBAHAN KHATAM ALANBIA UNIVERSITY OF TECHNOLOGY, BEHBAHAN, KHOUZESTAN, IRAN

2 DEPARTMENT OF MATHEMATICS, UNIVERSITY OF QOM, QOM 37161466711, IRAN

10.22103/jmmrc.2020.13904.1090

Abstract

In this paper we consider the one-dimensional variable-order time fractional diffusion equation where the order is $ q(x,t)\in (0,1) $. One type of Caputo fractional derivative is introduced and to get a numerical technique, the time variable is discretized using a
finite difference plan then we use a spectral collocation method to discretize the spatial derivative.‎ ‎In order to show the effectiveness and accuracy of this method‎, ‎some test problems are considered‎, ‎and it is shown that the obtained results are in very good agreement with exact solutions‎.

Keywords


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