Di erential transform method for solving two dimensional nonlinear systems of Volterra integral equations

In this paper, we will develop the two dimensional di erential transform method (DTM) for solvinga class of two dimensional nonlinear systems of Volterra integral equations of the second kind. Alsowe obtain an error bound for approximate solution which implies the convergence of this method.To this end we give some preliminary results of the di erential transform and describe the methodof this paper. If the system considered has a solution in terms of the series expansion of knownfunctions, this powerful method catches the exact solution. Also, to show capability and robustnessof the proposed method, some nonlinear systems of two dimensional volterra integral equations aresolved as numerical examples.