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A Collocation Method for Two-Point Boundary Value Problems
J. H. Ahlberg and T. Ito
Mathematics of Computation
Vol. 29, No. 131 (Jul., 1975), pp. 761-776
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2005287
Page Count: 16
You can always find the topics here!Topics: Textual collocation, Boundary value problems, Mathematical problems, Spline functions, Boundary conditions, Matrices, Galerkin methods, Coefficients, Mathematical functions
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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 band-width of the matrices involved. Comparisons are made to a similar approach using the Galerkin method rather than collocation.
Mathematics of Computation © 1975 American Mathematical Society