Two Numerical Methods for Solving Nonlinear Integral Equation in Two-Dimensional Problems

In this paper, the existence and uniqueness solution of nonlinear integral equations in two-dimensional problems is considered in the space 2 L (D)C (0,T ), where D is the domain of integration with respect to position, while t 0,T  , T 1 is the time. The equation takes a form of Fredholm- Volterra integral equation in nonlinear type (NFVIE). Here, we represent the unknown function in the form of Chebeyshev and Legendre polynomials and then, using Collocation and Galerkin methods, as two numerical methods, the numerical solutions of the NF-VIE are obtained. Numerical results are computed and the error, in each case is calculated