DE-sinc method for second order singularly perturbed boundary value problems. (English) Zbl 1169.65074

Summary: The sinc-Galerkin method, as well as the sinc-collocation method, based on the double exponential transformation (DE transformation) for singularly perturbed boundary value problems of second order ordinary differential equation is considered. A large merit of the present method exists in that we can apply the standard sinc method with only a small care for perturbation parameter. Through several numerical experiments we confirmed higher efficiency of the present method than that of other methods, e.g., sinc method based on the single exponential transformation, as the number of sampling points increases.


65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
34E15 Singular perturbations for ordinary differential equations
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
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