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Fitted Galerkin spectral method to solve delay partial differential equations
Author(s) -
Adam A. M. A.,
Bashier E. B. M.,
Hashim M. H. A.,
Patidar K. C.
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3756
Subject(s) - mathematics , partial differential equation , scalar (mathematics) , galerkin method , spectral method , parabolic partial differential equation , first order partial differential equation , delay differential equation , mathematical analysis , diffusion equation , differential equation , convection–diffusion equation , finite element method , geometry , physics , economy , service (business) , economics , thermodynamics
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.