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Splitting least squares and collocation procedures for two-point boundary value problems

Published online by Cambridge University Press:  17 February 2009

John Locker  and
P. M. Prenter
John Locker
Affiliation:
Department of Mathematics, Colorado State University, Fort Collins, Colorado 80523, U.S.A.
P. M. Prenter
Affiliation:
Department of Mathematics, Colorado State University, Fort Collins, Colorado 80523, U.S.A.
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Abstract

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Let L, T, S, and R be closed densely defined linear operators from a Hubert space X into X where L can be factored as L = TS + R. The equation Lu = f is equivalent to the linear system Tv + Ru = f and Su = v. If Lu = f is a two-point boundary value problem, numerical solution of the split system admits cruder approximations than the unsplit equations. This paper develops the theory of such splittings together with the theory of the Methods of Least Squares and of Collocation for the split system. Error estimates in both L2 and L∞ norms are obtained for both methods.

Type
Research Article
Information
The ANZIAM Journal , Volume 27 , Issue 2 , October 1985 , pp. 167 - 193
Copyright
Copyright © Australian Mathematical Society 1985

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