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Mathematics of Computation

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A comparison of some numerical methods for two-point boundary value problems

Author: James M. Varah
Journal: Math. Comp. 28 (1974), 743-755
MSC: Primary 65L10
MathSciNet review: 0373300
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Abstract: In this paper we discuss and compare two useful variable mesh schemes for linear second-order two-point boundary value problems: the midpoint rule and collocation with cubic Hermite functions. We analyze the stability of the block-tridiagonal factorization for solving the linear systems, compare the amount of computer time required, and test the methods on some particular numerical problems.

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Keywords: Two-point boundary value problems, collocation, Galerkin method, finite-differences, operation counts, numerical stability
Article copyright: © Copyright 1974 American Mathematical Society