Abstract
The objective of this paper is to present a comparative study of fitted-mesh finite difference method, B-spline collocation method and finite element method for general singularly perturbed two-point boundary value problems. Due to the small parameter ϵ , the boundary layer arises. We have taken a piecewise-uniform fitted-mesh to resolve the boundary layer and we have shown that fitted-mesh finite difference method has ϵ -uniform first order convergence, B-spline collocation method has almost second order ϵ -uniform convergence and Ritz–Galerkin method also has almost second order ϵ -uniform convergence. Two test examples have been solved to compare the maximum absolute error and rate of convergence of the methods.
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