Abstract
In this article, we create an effective technique fundamental on 2-dimensional Chelyshkov polynomials (2D-CPs) to expand an estimate solution of a type of 2-dimensional nonlinear Volterra integral equations (2D-NVIEs) of the primary type. This problem is changed to a 2D-NVIE of the 2 type and the technique transforms the integral equation to a system of nonlinear algebraic equations via implies of collocation points. At last, some numerical examples are given to clarify the efficiency of the presented strategy.