A second-order fitted operator finite difference method for a singularly perturbed delay parabolic partial differential equation

We design a parameter robust fitted operator finite difference method for the numerical solution of a singularly perturbed delay parabolic partial differential equation. The method is constructed by replacing the classical differential operator with a fitted operator based on Crank-Nicolson's d...

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Published in:Journal of difference equations and applications 2011-05, Vol.17 (5), p.779-794
Main Authors: Bashier, E.B.M., Patidar, K.C.
Format: Article
Language:English
Subjects:
Convergence
Delay
delay parabolic partial differential equation
Difference equations
Finite difference method
fitted operator finite difference methods
Mathematical analysis
Mathematical models
Operators
Parabolas
Partial differential equations
singular perturbations
stability
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description We design a parameter robust fitted operator finite difference method for the numerical solution of a singularly perturbed delay parabolic partial differential equation. The method is constructed by replacing the classical differential operator with a fitted operator based on Crank-Nicolson's discretization. The proposed method is analysed for stability and convergence and it is found that this method is unconditionally stable and is convergent with order , where k and h are respectively the time and space step sizes. The performance of this method is illustrated through a numerical example.
doi_str_mv 10.1080/10236190903305450
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subjects Convergence
Delay
delay parabolic partial differential equation
Difference equations
Finite difference method
fitted operator finite difference methods
Mathematical analysis
Mathematical models
Operators
Parabolas
Partial differential equations
singular perturbations
stability
title A second-order fitted operator finite difference method for a singularly perturbed delay parabolic partial differential equation
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