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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: 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
Email: jean-paul.kauthen@unifr.ch, kauthen@bluewin.ch

H. Brunner
Affiliation: Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, Newfoundland, Canada A1C 5S7
Email: hbrunner@morgan.ucs.mun.ca

DOI: http://dx.doi.org/10.1090/S0025-5718-97-00905-8
Keywords: Integral equation, collocation method, Runge-Kutta method
Received by editor(s): March 16, 1995
Article copyright: © Copyright 1997 American Mathematical Society