Numerical solutions of nonlinear quadratic Fredholm integral equations

Abstract

The two numerical techniques that will be introduced in this article to solve the (NQFIEs) are the Vieta-Lucas wavelets method (VLWM) and the Picard iteration method (PIM) associated with the Legendre-Gauss quadrature rule (LGQR). In the first place, we will show that the solution of the main problem exists and is unique under certain assumptions. Then, we use these two methods for solve the NQFIEs in two cases. Additionally, we estimate the VLWM convergence and error bound. Three numerical examples will be given to illustrate the efficiency and accuracy of solving NQFIEs using the two methods and comparing them.