Application of Legendre operational matrix to solution of two dimensional non-linear Volterra integro-differential equation

This article applies the operational matrix to find the numerical solution of two-dimensional nonlinear Volterra integrodifferential equation (2DNVIDE). Form this prospect, two-dimensional shifted Legendre functions (2DSLFs) have been presented for integration, product, and differentiation. This method converts 2DNVIDE to an algebraic system of equations, so the numerical solution of 2DNVIDE is computable. The effectiveness and accuracy of the method were examined with some examples as well. The results and comparison with other methods have shown remarkable performance.