Finite Difference Finite element and B-Spline Collocation Methods Applied to Two Parameter Singularly Perturbed Boundary Value Problems

M.K. Kadalbajoo and A.S.Yadaw2
Department of Mathematics and Statistics,
Indian Institute of Technology Kanpur,
Kanpur 208016, India
Received 9 December, 2009; accepted in revised form 20 December, 2010
Abstract: The objective of this paper is to present a comparative study of fitted-mesh finite
difference method, Ritz-Galerkin finite element method and B-spline collocation method
for a two-parameter singularly perturbed boundary value problems. Due to the small
parameters ? and ?, the boundary layers arise. We have taken a piecewise-uniform fittedmesh
to resolve the boundary layers and shown that fitted-mesh finite difference method
has almost first order parameter-uniform convergence, Ritz-Galerkin finite element method
has almost second order parameter-uniform convergence and B-spline collocation method
has second order parameter-uniform convergence. Numerical experiments support these
theoretical results.

 

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