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Fitted Galerkin spectral method to solve delay partial differential equations
- Source :
- Mathematical Methods in the Applied Sciences. 39:3102-3115
- Publication Year :
- 2015
- Publisher :
- Wiley, 2015.
-
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.
- Subjects :
- Partial differential equation
Differential equation
General Mathematics
Mathematical analysis
General Engineering
First-order partial differential equation
010103 numerical & computational mathematics
Delay differential equation
01 natural sciences
Parabolic partial differential equation
010101 applied mathematics
Elliptic partial differential equation
0101 mathematics
Spectral method
Hyperbolic partial differential equation
Mathematics
Subjects
Details
- ISSN :
- 01704214
- Volume :
- 39
- Database :
- OpenAIRE
- Journal :
- Mathematical Methods in the Applied Sciences
- Accession number :
- edsair.doi...........247c9acde2116ce61ac1b404c8c900b3