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 use interval functions to solve the NONLINEAR Fred, Holm INTEGRAL EQUATION of the second kind of the form: y(x)- b a∫g(x,t,y(x),y(t)dt=ƒ(x), xÎ[a,b] For solving above EQUATION with arithmetic functions, we know if INTEGRAL operator has some special properties, e.g. if INTEGRAL operator has monotonicity property, EQUATION will be easy solved. In this paper we will consider a general computational scheme, which does not assume any special properties of INTEGRAL operator.

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.

In the present paper, hybrid differential transform and finite difference method (HDTFD) is applied to solve 2D transient NONLINEAR straight annular fin EQUATION. For the case of linear heat transfer the results are verified with analytical solution. The effect of different parameters on in temperature distribution is investigated. Effect of time interval of differential transform on the stability of results has been examined. Results show the excellent capability of HDTFD to solve different engineering problems and also indicate that appropriate selection of differential transform time interval can solve the divergence problem of the method and lead to reduction in computational costs.