Summary
In the present paper integral equations of the first kind associated with strictly monotone Volterra integral operators are solved by projecting the exact solution of such an equation into the spaceS (−1) m (Z N ) of piecewise polynomials of degreem≧0, possessing jump discontinuities on the setZ N of knots. Since the majority of “direct” one-step methods (including the higher-order block methods) result from particular discretizations of the moment integrals occuring in the above projection method we obtain a unified convergence analysis for these methods; in addition, the above approach yields the tools to deal with the question of the connection between the location of the collocation points used to determine the projection inS (−1) m (Z N ) and the order of convergence of the method.
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This research was supported by the National Research Council of Canada (Grant No. A-4805)
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Brunner, H. Discretization of Volterra integral equations of the first kind (II). Numer. Math. 30, 117–136 (1978). https://doi.org/10.1007/BF02042940
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DOI: https://doi.org/10.1007/BF02042940