A collocation method for two-point boundary value problems

Authors:
J. H. Ahlberg and T. Ito

Journal:
Math. Comp. **29** (1975), 761-776

MSC:
Primary 65L10

DOI:
https://doi.org/10.1090/S0025-5718-1975-0375785-7

MathSciNet review:
0375785

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Abstract: This article is concerned with the use of collocation by splines to numerically solve two-point boundary value problems. The problem is analyzed in terms of cubic splines first and then extended to the use of quintic and septic splines. Consideration is given both to convergences as the mesh is refined and to the bandwidth of the matrices involved. Comparisons are made to a similar approach using the Galerkin method rather than collocation.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1975-0375785-7

Keywords:
Collocation,
two-point boundary value problems,
spline,
*B*-spline,
diagonally dominant,
order of convergence,
nonlinear system,
Lipschitz condition,
quintic splines,
spline of interpolation,
septic splines,
bandwidth

Article copyright:
© Copyright 1975
American Mathematical Society