Document Type : Research Articles


1 Department of Mathematics, North Tehran Branch, Islamic Azad University, Tehran, Iran

2 Department of Mathematics, Payame Noor University, P.O. Box 19395-3697 Tehran, Iran

3 Department of Mathematics, Firoozkooh Branch, Islamic Azad University, Firoozkooh, Iran


In this article, we apply the operational matrix to find the numerical solution of two- dimensional nonlinear Volterra integro-differential equation (2DNVIDE). Form this prospect, two-dimensional shifted Legendre functions (2DSLFs) has been presented for integration, product as well as 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 a remarkable performance.