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On global superconvergence of iterated collocation solutions to linear second-kind Volterra integral equations. (English) Zbl 0857.65145

Iterated collocation solutions for Volterra integral equations of the second kind with optimal superconvergence and numerical illustration are presented.

MSC:

65R20 Numerical methods for integral equations
45G10 Other nonlinear integral equations
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References:

[1] Blom, J. G.; Brunner, H., The numerical solution of nonlinear Volterra integral equations of the second kind by collocation and iterated collocation methods, SIAM J. Sci. Statist. Comput., 8, 806-830 (1987) · Zbl 0629.65144
[2] Brunner, H., Iterated collocation methods and their discretizations for Volterra integral equations, SIAM J. Numer. Anal., 21, 1132-1145 (1984) · Zbl 0575.65134
[3] Brunner, H., On discrete superconvergence properties of spline collocation methods for nonlinear Volterra integral equations, J. Comput. Math., 10, 348-357 (1992) · Zbl 0758.65083
[4] Brunner, H.; van der Houwen, P. J., The Numerical Solution of Volterra Equations, (CWI Monographs, Vol. 3 (1986), North-Holland: North-Holland Amsterdam) · Zbl 0611.65092
[5] Chatelin, F.; Lebbar, R., The iterated projection solution for the Fredholm integral equation of the second kind, J. Austral. Math. Soc. Ser. B, 22, 439-451 (1981) · Zbl 0472.65093
[6] Joe, S., Collocation methods using piecewise polynomials for second kind integral equations, J. Comput. Appl. Math., 12/13, 391-400 (1985) · Zbl 0586.65090
[7] Sloan, I. H., Superconvergence, (Golberg, M. A., Numerical Solution of Integral Equations (1990), Plenum Press: Plenum Press New York), 35-70 · Zbl 0759.65091
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