Finite Difference, Finite element and B-Spline Collocation Methods Applied to Two Parameter Singularly Perturbed Boundary Value Problems
نویسندگان
چکیده
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 ε 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. c ⃝ 2011 European Society of Computational Methods in Sciences and Engineering
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