a b s t r a c tIn this paper, we will give some results for developing the two-dimensional differential transform (TDDT) for double integrals. Then the TDDT method will be developed for solving a class of two-dimensional linear and nonlinear Volterra integral equations. We also give some examples to demonstrate the accuracy of the method.

In this paper an expansion method, based on Legendre or any orthogonal polynomials, is developed to find numerical solutions of two-dimensional linear Fredholm integral equations. We estimate the error of the method, and present some numerical examples to demonstrate the accuracy of the method.2000 Mathematics subject classification: 65R20.

-In this paper, we consider a general form of two-dimensional linear Volterra integro-differential equations(TDLVIDE) of the second order with some supplementary conditions and develop the operational Tau method with standard base for obtaining a numerical solution.2000 Mathematics Subject Classification: 65R20.

a b s t r a c tIn this paper, we develop the differential transform method (DTM) for solving a class of the system of two-dimensional linear and nonlinear Volterra integro-differential equations of the second kind. To this end, we give some preliminary results of the differential transform and describe the method of this paper. We also give some examples to demonstrate the accuracy of the presented method.

In this paper, we develop the operational Tau method for solving nonlinear Volterra integro-differential equations of the second kind. The existence and uniqueness of the problem is provided. Here, we show that the nonlinear system resulted from the operational Tau method has a semi triangular form, so it can be solved easily by the forward substitution method. Finally, the accuracy of the method is verified by presenting some numerical computations.