Numerical Treatment of Singularly Perturbed Delay Differential Equations Using B-Spline Collocation Method on Shishkin Mesh

Devendra Kumar, M.K. Kadalbajoo
Received 5 August, 2011; accepted in revised form 22 July, 2012
Abstract: This paper is devoted to the numerical study for a class of boundary value
problems of second-order differential equations in which the highest order derivative is
multiplied by a small parameter ? and both the convection and reaction terms are with
negative shift. To obtain the parameter-uniform convergence, a piecewise uniform mesh
(Shishkin mesh) is constructed, which is dense in the boundary layer region and coarse in
the outer region. Parameter-uniform convergence analysis of the method has been given.
The method is shown to have almost second-order parameter-uniform convergence. The
effect of small delay ? on the boundary layer has also been discussed. To demonstrate the
performance of the proposed scheme several examples having boundary layers have been
carried out. The maximum absolute errors are presented in the tables.


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