A uniformly convergent exponential spline difference scheme for singularly perturbed reaction-diffusion problems

Authors:
S. Chandra Sekhara Rao;Mukesh Kumar
Affiliations:
Department of Mathematics, Indian Institute of Technology Delhi, New Delhi, India;Department of Mathematics, Indian Institute of Technology Delhi, New Delhi, India
Venue:
Neural, Parallel & Scientific Computations
Year:
2010

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Abstract

We consider a Dirichlet boundary value problem for singularly perturbed reaction-diffusion equation. The problem is discretized using an exponential spline difference scheme derived on the basis of splines in tension. The fitted mesh technique is employed to generate piecewise-uniform Shishkin type mesh, condensed in the neighborhood of the boundary layers. The convergence analysis is given and the method is shown to have second order ε-uniform convergence on piecewise-uniform Shishkin type mesh. Numerical experiments are conducted to demonstrate the theoretical results.