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

DOI:
https://doi.org/10.1090/S0025-5718-1984-0744929-2

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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DOI:
https://doi.org/10.1090/S0025-5718-1984-0744929-2

Article copyright:
© Copyright 1984
American Mathematical Society