On the Effect of Boundary Conditions in Collocation by Polynomial Splines for the Solution of Boundary Value Problems in Ordinary Differential Equations
- 1 August 1975
- journal article
- Published by Oxford University Press (OUP) in IMA Journal of Applied Mathematics
- Vol. 16 (1) , 93-107
- https://doi.org/10.1093/imamat/16.1.93
Abstract
Consider the numerical solution of a boundary-value problem for a differential equation of order m using collocation of a polynomial spline of degree n ≧ m on a uniform mesh of size h. We describe several collocation schemes which differ only in the boundary collocation conditions and which include a “natural” spline collocation scheme. Taking account of derived asymptotic error bounds most of which are, roughly speaking, of O(hn12 m+1), we discuss the computational effectiveness of the various schemes.Keywords
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