The iterative correction method for Volterra integral equations. (English) Zbl 0854.65121

The authors apply an iterative correction method to the iterated collocation solution for a Volterra integral equation of the second kind. With the \((n-1)\)st correction for the one-point iterated collocation solution, the error can be improved to \(O(h^n)\). The presented theory is illustrated by a numerical example.
Reviewer: L.Hącia (Poznań)


65R20 Numerical methods for integral equations
45D05 Volterra integral equations
Full Text: DOI


[1] K. Atkinson and J. Flores,The discrete collocation method for nonlinear integral equations, IMA J. Numer. Anal., 13 (1993), 195–213. · Zbl 0771.65090
[2] H. Brunner,Iterated collocation methods and their discretizations for Volterra integral equations, SIAM J. Numer. Anal., 21 (1984), 1132–1145. · Zbl 0575.65134
[3] H. Brunner,Collocation methods for one-dimensional Fredholm and Volterra integral equations, in The State of the Art in Numerical Analysis, A. Iserles and M. J. D. Powell, eds., Oxford University Press, Oxford, 1987, 563–600.
[4] H. Brunner,On discrete superconvergence properties of spline collocation methods for nonlinear Volterra integral equations, J. Comput. Math., 10 (1992), 348–357. · Zbl 0758.65083
[5] Q. Lin and J. Shi,Iterative corrections and posteriori error estimate for integral equations, J. Comput. Math., 11 (1993), 297–300. · Zbl 0789.65040
[6] I. H. Sloan,Superconvergence, in Numerical Solution of Integral Equations, M. A. Golberg, ed., pp. 35–70, Plenum Press, New York, 1990.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.