Article ID Journal Published Year Pages File Type
4623801 Journal of Mathematical Analysis and Applications 2006 13 Pages PDF
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.

Related Topics
Physical Sciences and Engineering Mathematics Analysis