A different approach for solving the nonlinear Fredholm integral equations of the second kind

The numerical method of successive interpolations for Fredholm functional integral equations

“…for all i = 0, n. According to the contraction condition (iii), we get the inequality (22). (22), since lim…”

“…For the numerical solution of Fredholm integral equations, Galerkin methods are used in [8,9,12,14,46] and [53]. Other methods use spline functions and wavelets (see [5,46,47,50]), product integration (see [9,29]), homotopy analysis techniques (see [2]), homotopy perturbation and Adomian decomposition method (see [3] and [18]), polynomial interpolation procedures and suboptimal trajectories (see [22] and [26]), multigrid methods (see [9,39]). Nyström techniques are used in [8,9,15,16,28,48] and [58].…”

Rationalized Haar wavelet bases to approximate solution of nonlinear Fredholm integral equations with error analysis

“…The comparison between the approximate solutions obtained by our Haar wavelet method, with the methods in [10] and [11] is given in Table 2. We see that there is a good agreement in the results between these methods.…”

Approximate Solution Of A Class Of Nonlinear Volterra Integral Equations

“…The problem of finding numerical solution for integral equation is one of the oldest problems in applied mathematics and many computational methods are proposed in this area (see [1], [3] and [5] xT   .The necessary and sufficient conditions of existence and uniqueness of the solution for the above problem can be found in [8]. Here, it is assumed that the problem, which is being considered.…”