Parameter-Uniformly Convergent Hybrid Scheme for Singularly Perturbed Boundary Value Problems
by
Mukesh Kumar
Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi-110 016, India
Coauthors: S. Chandra Sekhara Rao

We introduce a parameter uniformly convergent hybrid scheme for singularly perturbed boundary value problems. The proposed hybrid scheme is a modified version of the simple midpoint upwind scheme. The present hybrid scheme is a combination of the cubic spline based difference scheme and the midpoint upwind scheme on a special non-uniform Shishkin type mesh. Numerical results show that the convergence of the proposed hybrid scheme is uniform with respect to the singular perturbation parameter and has a higher order convergence in comparison with the simple midpoint upwind scheme on a special non-uniform Shishkin type mesh.

Date received: February 14, 2007