A numerical solution of nonlinear Fredholm using Haar wavelets

In this paper, a new algorithms based on Haar wavelets are proposed. This algorithm is proposed for the numerical solution of nonlinear Fredholm integral equations of the second kind. This method are designed to exploit the special characteristics of Haar wavelets in both one and two dimensions. Formulae for calculating Haar coefficients without solving the system of equations have been derived. These formulae are then used in the proposed numerical methods. In contrast to other numerical methods, the advantage of our method is that it does not involve any intermediate numerical technique for evaluation of the integral present in integral equations. The methods are validated on test problems, and numerical results are compared with those from existing methods in the literature.

کلیدواژه ها:

: numerical solution ، Haar wavelets ، Fredholm integral equations