Numerical algorithm for singularly perturbed delay differential equations with layer and oscillatory behavior

Authors:
V. P. Ramesh;M. K. Kadalbajoo
Affiliations:
Department of Mathematics & Statistics, Indian Institute of Technology Kanpur, India;Department of Mathematics & Statistics, Indian Institute of Technology Kanpur, India
Venue:
Neural, Parallel & Scientific Computations
Year:
2011

Citing 3
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Sufficient conditions for the uniform convergence of a difference scheme for a singularly perturbed turning point problem

SIAM Journal on Numerical Analysis
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Singular perturbation analysis of boundary-value problems for differential-difference equations. VI.: small shifts with rapid oscillations

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Abstract

We consider the numerical approximation of singularly perturbed linear second order reaction-diffusion boundary value problems with a small shift(δ) in the undifferentiated term and the shift depends on the small parameter(ε). The presence of small parameter induces twin boundary layers. The problem is discretized using standard finite difference scheme on an uniform mesh and the retarded arguments are interpolated/extrapolated using the known computational grid points. We present a new algorithm to interpolate/exptrapolate the retarded term in terms of its neighbouring points. The scheme is proved to be stable and the error estimate is also given. It is shown that the shift has significant effect on the behavior of the solution. Numerical experiments are performed to support both the theoretical results as well as the existing results in the literature.