Learn 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)
A multiscale collocation method is developed for solving the eigen-problem of weakly singular integral operators. We employ a matrix truncation strategy of Chen, Micchelli and Xu to compress the collocation matrix, which the compressed matrix has only O(N logN) nonzero entries, where N denotes the order of the matrix. This truncation leads to a fast(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)