Discretization of Volterra integral equations of the first kind

Brunner, Hermann

doi:10.1090/S0025-5718-1977-0451794-6

Discretization of Volterra integral equations of the first kind
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Math. Comp. 31 (1977), 708-716 Request permission

Abstract:

We show that various (discrete) methods for the approximate solution of Volterra (and Abel) integral equations of the first kind correspond to some discrete version of the method of (recursive) collocation in the space of (continuous) piecewise polynomials. In a collocation method no distinction has to be made between equations with regular or weakly singular kernels; the regularity or nonregularity of the given integral operator becomes only relevant when selecting a discretization procedure for the moment integrals resulting from collocation. Similar results hold for equations of the second kind.

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The Numerical Solution of Differential and Integral Equations by Spline Functions

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