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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Collocation for singular perturbation problems. II. Linear first order systems without turning points

Authors: U. Ascher and R. Weiss
Journal: Math. Comp. 43 (1984), 157-187
MSC: Primary 65L10; Secondary 34E15
MathSciNet review: 744929
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Abstract: We consider singularly perturbed linear boundary value problems for ODE's with variable coefficients, but without turning points. Convergence results are obtained for collocation schemes based on Gauss and Lobatto points, showing that highly accurate numerical solutions for these problems can be obtained at a very reasonable cost using such schemes, provided that appropriate meshes are used. The implementation of the numerical schemes and the practical construction of corresponding meshes are discussed.

These results extend those of a previous paper which deals with systems with constant coefficients.

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Article copyright: © Copyright 1984 American Mathematical Society