Extrapolation method for solving weakly singular nonlinear Volterra integral equations of the second kind (Q855631)

The authors present a new extrapolation method for solving weakly singular nonlinear Volterra integral equations of the second kind based on a discreet Gronwall inequality [created by \textit{L.Tao} and \textit{H. Young}, ibid. 282, No. 1, 56--62 (2003; Zbl 1030.65140)], further \textit{I. Navot}'s quadrature rule [J. Math. Phys. 41, 155--163 (1962; Zbl 0109.28904)]for computing integrals with endpoint singularity. The method is based on a quadrature method given by the authors for the same case. The convergence of the approximation solution is proved. An asymptotic expansion of the error is also given.