THE REDUCED DIFFERENTIAL TRANSFORM METHOD IS ONE OF THE APPROXIMATE METHODS WHICH CAN BE EASILY APPLIED TO MANY LINEAR AND NONLINEAR PROBLEMS AND IS CAPABLE OF REDUCING THE SIZE OF COMPUTATIONAL WORK. EXACT SOLUTIONS CAN ALSO BE ACHIEVED BY THE KNOWN FORMS OF THE SERIES SOLUTIONS. THE METHOD CAN EASILY BE APPLIED TO MANY LINEAR AND NON-LINEAR PROBLEMS AND IS CAPABLE OF REDUCING THE SIZE OF COMPUTATIONAL WORK. EXACT SOLUTIONS CAN ALSO BE ACHIEVED BY THE KNOWN FORMS OF THE SERIES SOLUTIONS. SEVERAL ILLUSTRATIVE EXAMPLES ARE GIVEN TO DEMONSTRATE THE EFFECTIVENESS OF THE PRESENT METHOD.

THE PROBLEM ADDRESSED IN THIS PAPER IS SOLVING LINEARAND NONLINEAR DIFFERENTIAL-DIFFERENCE EQUATIONS BY USING OF AN AUXILIARY PARAMETER METHOD USING DIFFERENTIAL TRANSFORM METHOD ANDADOMIAN POLYNOMIALS. SO, THE METHOD HERE AFTER IS CALLED AUXILIARY DIFFERENTIAL TRANSFORM PARAMETER METHOD (ADTPM).

This paper employs the DIFFERENTIAL TRANSFORMation technique to solve the two-dimensional Volterra integro DIFFERENTIAL equations. By extension of the operations, a two-dimensional intego-DIFFERENTIAL equation in the domain of interest can be TRANSFORMed into a system of algebraic equations. The approximations of these equations are calculated in the form of a series with easy computable terms. Exact solutions can also be achieved by the known forms of the series solutions. The method can be easily applied to many linear and non linear problems. Some illustrative examples are given to demonstrate the effectiveness of the present method.