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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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


Authors: I. A. Blatov and V. V. Strygin
Journal: Math. Comp. 68 (1999), 683-715
MSC (1991): Primary 65-02, 65L99; Secondary 65G99, 45A10
MathSciNet review: 1620211
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

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: http://dx.doi.org/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
Article copyright: © Copyright 1999 American Mathematical Society