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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)


Continuous collocation approximations
to solutions of first kind Volterra equations

Authors: J.-P. Kauthen and H. Brunner
Journal: Math. Comp. 66 (1997), 1441-1459
MSC (1991): Primary 65R20, 45L10
MathSciNet review: 1434941
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we give necessary and sufficient conditions for convergence of continuous collocation approximations of solutions of first kind Volterra integral equations. The results close some longstanding gaps in the theory of polynomial spline collocation methods for such equations. The convergence analysis is based on a Runge-Kutta or ODE approach.

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Additional Information

J.-P. Kauthen
Affiliation: Institut de Mathématiques, Université de Fribourg, CH-1700 Fribourg, Switzerland

H. Brunner
Affiliation: Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, Newfoundland, Canada A1C 5S7

PII: S 0025-5718(97)00905-8
Keywords: Integral equation, collocation method, Runge-Kutta method
Received by editor(s): March 16, 1995
Article copyright: © Copyright 1997 American Mathematical Society

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