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http://dx.doi.org/10.14317/jami.2022.603

HIGHER ORDER GALERKIN FINITE ELEMENT METHOD FOR THE GENERALIZED DIFFUSION PDE WITH DELAY  

LUBO, GEMEDA TOLESSA (Department of Mathematics, Wollega University)
DURESSA, GEMECHIS FILE (Department of Mathematics, College of Natural Sciences, Jimma University)
Publication Information
Journal of applied mathematics & informatics / v.40, no.3_4, 2022 , pp. 603-618 More about this Journal
Abstract
In this paper, a numerical solution of the generalized diffusion equation with a delay has been obtained by a numerical technique based on the Galerkin finite element method by applying the cubic B-spline basis functions. The time discretization process is carried out using the forward Euler method. The numerical scheme is required to preserve the delay-independent asymptotic stability with an additional restriction on time and spatial step sizes. Both the theoretical and computational rates of convergence of the numerical method have been examined and found to be in agreement. As it can be observed from the numerical results given in tables and graphs, the proposed method approximates the exact solution very well. The accuracy of the numerical scheme is confirmed by computing L2 and L∞ error norms.
Keywords
Generalized diffusion equation; finite element; cubic B-spline; forward Euler;
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