The piecewise polynomial collocation method for nonlinear weakly singular Volterra equations

Brunner, Hermann; Pedas, Arvet; Vainikko, Gennadi

doi:10.1090/S0025-5718-99-01073-X

The piecewise polynomial collocation method for nonlinear weakly singular Volterra equations
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by Hermann Brunner, Arvet Pedas and Gennadi Vainikko PDF

Math. Comp. 68 (1999), 1079-1095 Request permission

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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