A robust numerical method for singularly perturbed semilinear convection-diffusion problems

Authors:
S. Chandra Sekhara Rao;S. 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

A singularly perturbed semilinear convection-diffusion problem is considered. The leading term is multiplied by a small positive parameter ε. The solution to this problem exhibits boundary layer at the left end of the domain. To solve this problem numerically, we develop a B-spline collocation method on a piecewise-uniform Shishkin mesh. The error analysis is given and the method is proved to be almost second-order convergent in the maximum norm uniformly in ε. Numerical results are presented in support of the theory.