Mathematics of Computation

On best possible order of convergence estimates in the collocation method and Galerkin's method for singularly perturbed boundary value problems for systems of first-order ordinary differential equations

Author(s): I. A. Blatov; V. V. Strygin.
Journal: Math. Comp. 68 (1999), 683-715.
MSC (1991): Primary 65-02, 65L99; Secondary 65G99, 45A10
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Abstract: The collocation method and Galerkin method using parabolic splines are considered. Special adaptive meshes whose number of knots is independent of the small parameter of the problem are used. Unimprovable estimates in the $L_\infty$ -norm are obtained. For the Galerkin method these estimates are quasioptimal, while for the collocation method they are suboptimal.

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Retrieve articles in Mathematics of Computation with MSC (1991): 65-02, 65L99, 65G99, 45A10

I. A. Blatov
Affiliation: Department of Applied Mathematics and Mechanics, Voronezh State University, Universitetskaya pl.1, Voronezh, Russia, 394693
Email: blatov@kvm.vsu.ru

V. V. Strygin
Affiliation: Department of Applied Mathematics and Mechanics, Voronezh State University, Universitetskaya pl.1, Voronezh, Russia, 394693
Email: strygin@kvm.vsu.ru

DOI: 10.1090/S0025-5718-99-01034-0
PII: S 0025-5718(99)01034-0
Keywords: Finite element method for singular perturbation problems, collocation method, Galerkin method
Received by editor(s): May 28, 1994
Received by editor(s) in revised form: February 11, 1995 and May 26, 1996
Copyright of article: Copyright 1999, American Mathematical Society

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