Approximate Solutionof Space Fractional Order Difusion Equation
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Date
2023-05
Journal Title
Journal ISSN
Volume Title
Publisher
Journal of the Nigerian Society of Physical Sciences (JNSPS)
Abstract
J. Nig. Soc. Phys. Sci. 5 (2023) 1368
Journal of the
Nigerian Society
of Physical
Sciences
Approximate solution of space fractional order diffusion
equations by Gegenbauer collocation and compact finite
difference scheme
K. Issa∗, A. S. Olorunnisola, T. O. Aliu, A. D. Adeshola
Department of Mathematics and Statistics, Kwara State University, Malete, Kwara State, Nigeria.
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 β− 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