Continuous collocation approximations to solutions of first kind Volterra equations

Kauthen, J.-P.; Brunner, H.

doi:10.1090/S0025-5718-97-00905-8

Continuous collocation approximations to solutions of first kind Volterra equations
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by J.-P. Kauthen and H. Brunner PDF

Math. Comp. 66 (1997), 1441-1459 Request permission

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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