A finite-difference method for a singularly perturbed delay integro-differential equation

We consider the singularly perturbed initial value problem for a linear first order Volterra integro-differential equation with delay. Our purpose is to construct and analyse a numerical method with uniform convergence in the perturbation parameter. The numerical solution of this problem is discreti...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2016-12, Vol.308, p.379-390
Main Authors: Kudu, Mustafa, Amirali, Ilhame, Amiraliyev, Gabil M.
Format: Article
Language:English
Subjects:
Approximation
Convergence
Delay
Delay difference scheme
Finite difference method
Initial value problems
Layer adapted mesh
Mathematical analysis
Mathematical models
Perturbation methods
Singular perturbation
Uniform convergence
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Summary:We consider the singularly perturbed initial value problem for a linear first order Volterra integro-differential equation with delay. Our purpose is to construct and analyse a numerical method with uniform convergence in the perturbation parameter. The numerical solution of this problem is discretized using implicit difference rules for differential part and the composite numerical quadrature rules for integral part. On a layer-adapted mesh error estimations for the approximate solution are established. Numerical examples supporting the theory are presented.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2016.06.018