Approximate solution of space fractional order diffusion equations by Gegenbauer collocation and compact finite difference scheme: Solution of space fractional diffusion equation

Kazeem Issa; Steven  Ademola Olorunnisola; Tajudeen Aliu; Adeshola Adeniran Dauda

doi:10.46481/jnsps.2023.1368

Authors

K. Issa
[email protected]

Department of Mathematics and Statistics, Kwara State University, Malete, Kwara State, Nigeria.
A. S. Olorunnisola
Department of Mathematics and Statistics, Kwara State University, Malete, Kwara State, Nigeria.
O. T. Aliu
Department of Mathematics and Statistics, Kwara State University, Malete, Kwara State, Nigeria.
A. D. Adeshola
Department of Mathematics and Statistics, Kwara State University, Malete, Kwara State, Nigeria.

Keywords:

Caputo derivative, fractional diffusion equation, Gegenbauer polynomial, Compact finite difference method (CFDM)

Abstract

In this paper, approximation of space fractional order diffusion equation are considered using compact finite difference technique to discretize the time derivative, which was then approximated via shifted Gegenbauer polynomials using zeros of (N - 1) degree shifted Gegenbauer polynomial as collocation points. The important feature in this approach is that it reduces the problems to algebraic linear system of equations together with the boundary conditions gives (N + 1) linear equations. Some theorems are given to establish the convergence and the stability of the proposed method. To validate the efficiency and the accuracy of the method, obtained results are compared with the existing results in the literature. The graphical representation are also displayed for various values of \beta Gegenbauer polynomials. It can be observe in the tables of the results and figures that the proposed method performs better than the existing one in the literature.

Dimensions

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