An efficient wavelet-based numerical method to solve nonlinear Fredholm integral equation of second kind with smooth kernel

In this paper, a wavelet-based numerical algorithm is described to obtain approximate numerical solution of a class of nonlinear Fredholm integral equations of second kind having smooth kernels. The algorithm involves  approximation of the unknown function in terms of Daubechies scale functions. The properties of Daubechies scale and wavelet functions together with one-point quadrature rule for the product of a smooth function and Daubechies scale functions are utilized to transform the integral equation to a system of nonlinear equations. The efficiency of the proposed method is demonstrated through three illustrative examples.