In this paper, a numerical method for solving the NONLINEAR FREDHOLM INTEGRAL EQUATION is presented. We intend to approximate the solution of this EQUATION by quadrature methods and by doing so, we solve the NONLINEAR FREDHOLM INTEGRAL EQUATION more accurately. Several examples are given at the end of this paper.

In this paper, we have used Chebyshev polynomials to solve linear and NONLINEAR Volterra-FREDHOLM INTEGRAL EQUATIONs, numerically. First we introduce these polynomials, then we use them to change the Volterra-FREDHOLM INTEGRAL EQUATION to a linear or NONLINEAR system. Finally, the numerical examples illustrate the effi ciency of this method.

A new six order method developed for the approximation FREDHOLM INTEGRAL EQUATION of the second kind. This method is based on the quintic spline functions (QSF). In our approach, we , rst formulate the Quintic polynomial spline then the solution of INTEGRAL EQUATION approximated by this spline. But we need to develop the end conditions which can be associated with the quntic spline. To avoid the reduction accuracy, we formulate the end condition in such a way to obtain the band matrix and also to obtain the same order of accuracy. The convergence of the method is discussed by using matrix algebra. Finally, four test problems have been used for numerical illustration to demonstrate the practical ability of the new method.

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In this paper, we compute the approximate numerical solution for the Volterra-FREDHOLM INTEGRAL EQUATION (VFIE) by using the shifted Jacobi collocation (SJC) method which depends on the operational matrices. Some properties of the shifted Jacobi polynomials are introduced. These properties allow us to transform the VolterraFREDHOLM INTEGRAL EQUATION into a system of algebraic EQUATIONs in a nice form with the expansion coefficients of the solution. Also, the convergence and error analysis are studied extensively. Finally, some examples which verify the efficiency of the given method are supplied and compared with other methods.

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.

In this paper, we propose a numerical method based on the generalized hat functions (GHFs) and improved hat functions (IHFs) to find numerical solutions for stochastic Volterra-FREDHOLM INTEGRAL EQUATION. To do so, all known and unknown functions are expanded in terms of basic functions and replaced in the original EQUATION. The operational matrices of both basic functions are calculated and embeded in the EQUATION to achieve a linear system of EQUATIONs which give the expansion coefficients of the solution. We prove that the rate of the convergence is O(h2) and O(h4) for these two different bases under some conditions. Two examples are solved and the results are compared with those of block pulse functions method (BPFs) to show the accuracy and reliability of the methods.