Abstract :
Based on a new generalization of discrete Gronwall inequality in [L. Tao, H. Yong, A generalization of
discrete Gronwall inequality and its application to weakly singular Volterra integral equality of the second
kind, J. Math. Anal. Appl. 282 (2003) 56–62], Navot’s quadrature rule for computing integrals with the
end point singularity in [I. Navot, A further extension of Euler–Maclaurin summation formula, J. Math.
Phys. 41 (1962) 155–184] and a transformation in [P. Baratella, A. Palamara Orsi, A new approach to
the numerical solution of weakly singular Volterra integral equations, J. Comput. Appl. Math. 163 (2004)
401–418], a new quadrature method for solving nonlinear weakly singular Volterra integral equations of the
second kind is presented. The convergence of the approximation solution and the asymptotic expansion of
the error are proved, so by means of the extrapolation technique we not only obtain a higher accuracy order
of the approximation but also get a posteriori estimate of the error.
© 2005 Elsevier Inc. All rights reserved.
