Finite difference, finite element and B-spline collocation methods applied to two parameter singularly perturbed boundary value problems

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 μ, 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.