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Continuous collocation approximations to solutions of first kind Volterra equations |
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| Authors: | J-P Kauthen H Brunner |
| Institution: | Institut de Mathématiques, Université de Fribourg, CH-1700 Fribourg, Switzerland ; Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, Newfoundland, Canada A1C 5S7 |
| 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. |
| Keywords: | Integral equation collocation method Runge-Kutta method |
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