In this paper, we present a new computational method for solving nonlinear Fredholm integral equations of the second kind with weakly singular kernels. The adaptation of Chebyshev wavelets to discrete Galerkin method for solving weakly singular integral equations has more difficulties to compute the appeared singular integrals due to the presence of the weight function. To overcome these problems, we introduce the dual-Chebyshev wavelets constructed on the unit interval which are orthonormal without any weight functions. Therefore, the implementation of dual-Chebyshev wavelets in the discrete Galerkin method leads to a far easier scheme to estimate weakly singular integrals. The method developed in the current paper approximates these integrals using the non-uniform Gauss-Legendre quadrature rule. The error estimate and the rate of convergence of the method are presented. Finally, numerical examples are included to show the validity and efficiency of the new technique.
