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

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:
https://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