Mathematics of Computation

The piecewise polynomial collocation method for nonlinear weakly singular Volterra equations

Author(s): Hermann Brunner; Arvet Pedas; Gennadi Vainikko.
Journal: Math. Comp. 68 (1999), 1079-1095.
MSC (1991): Primary 65R20, 45E10, 45B05
Posted: February 8, 1999
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Abstract: Second-kind Volterra integral equations with weakly singular kernels typically have solutions which are nonsmooth near the initial point of the interval of integration. Using an adaptation of the analysis originally developed for nonlinear weakly singular Fredholm integral equations, we present a complete discussion of the optimal (global and local) order of convergence of piecewise polynomial collocation methods on graded grids for nonlinear Volterra integral equations with algebraic or logarithmic singularities in their kernels.

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Retrieve articles in Mathematics of Computation with MSC (1991): 65R20, 45E10, 45B05

Hermann Brunner
Affiliation: Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, Nfld., Canada A1C 5S7
Email: hermann@math.mun.ca

Arvet Pedas
Affiliation: Department of Applied Mathematics, University of Tartu, 0000 Liivi 2--206, Tartu EE2400, Estonia
Email: Arvet.Pedas@ut.ee

Gennadi Vainikko
Affiliation: Institute of Mathematics, Helsinki University of Technology, P.O.Box 1100, FIN--02015 HUT, Finland
Email: Gennadi.Vainikko@hut.fi

DOI: 10.1090/S0025-5718-99-01073-X
PII: S 0025-5718(99)01073-X
Keywords: Nonlinear weakly singular Volterra and Fredholm integral equations, piecewise polynomial collocation, graded grids, optimal order of convergence
Received by editor(s): September 2, 1997
Posted: February 8, 1999
Copyright of article: Copyright 1999, American Mathematical Society

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