Fitted Galerkin spectral method to solve delay partial differential equations |
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| Authors: | A. M. A. Adam E. B. M. Bashier M. H. A. Hashim K. C. Patidar |
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| Affiliation: | 1. Department of Mathematics, Faculty of Sciences, Northern Border University, Arar, Kingdom of Saudi Arabia;2. Department of Mathematics, Physics and Statistics, College of Arts and Sciences, Doha, Qatar;3. Department of Mathematics and Applied Mathematics, University of the Western Cape, Bellville, South Africa |
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| Abstract: | ![]()
In this paper, we consider a class of parabolic partial differential equations with a time delay. The first model equation is the mixed problems for scalar generalized diffusion equation with a delay, whereas the second model equation is a delayed reaction‐diffusion equation. Both of these models have inherent complex nature because of which their analytical solutions are hardly obtainable, and therefore, one has to seek numerical treatments for their approximate solutions. To this end, we develop a fitted Galerkin spectral method for solving this problem. We derive optimal error estimates based on weak formulations for the fully discrete problems. Some numerical experiments are also provided at the end. Copyright © 2015 John Wiley & Sons, Ltd. |
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| Keywords: | delay partial differential equations reaction‐diffusion equations Galerkin spectral method convergence analysis error estimate subclass 35R10 65M15 65M70 |
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