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...

Full description

Saved in:
Bibliographic Details
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
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:1023-6198
1563-5120
DOI:10.1080/10236190903305450