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We apply Adomian decomposition method (ADM) for obtaining approximate series solution of Urysohn integral equations. The ADM provides a direct recursive scheme for solving such problems approximately. The approximations of the solution are obtained in the form of series with easily calculable components. Furthermore, we also discuss the convergence and(More)
Copyright q 2012 Randhir Singh et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We propose two new modified recursive schemes for solving a class of doubly singular two-point boundary(More)
In this paper, we consider the Legendre spectral Galerkin and Legendre spectral collocation methods to approximate the solution of Urysohn integral equation. We prove that the approximated solutions of the Legendre Galerkin and Legendre collocation methods converge to the exact solution with the same orders, O(n −r) in L 2-norm and O(n 1 2 −r) in infinity(More)