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Mathematics of Computation

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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
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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Keywords: Collocation, two-point boundary value problems, spline, <I>B</I>-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