This work presents solution of nonlinear differential-difference equations such as the discretized mKdV lattice equation, the discretized nonlinear Schrödinger equation and the Toda Lattice equation by Differential Transformation Method (DTM). This method provides more realistic solutions by solving the nonlinear differential equations without any simplification and the series solutions which generally converge very rapidly in real physical models. Moreover, no linearization or perturbation is required in this method. By using this method, exact solutions may be obtained without any need of cumbersome work. This method is a useful tool for analytical and numeric solutions. The results of the present method are compared with those obtained by Adomian Decomposition Method and exact solutions. The results have shown that DTM method has better performs.

This work presents solution of nonlinear differential-difference equations such as the discretized mKdV lattice equation, the discretized nonlinear Schrödinger equation and the Toda Lattice equation by Differential Transformation Method (DTM). This method provides more realistic solutions by solving the nonlinear differential equations without any simplification and the series solutions which generally converge very rapidly in real physical models. Moreover, no linearization or perturbation is required in this method. By using this method, exact solutions may be obtained without any need of cumbersome work. This method is a useful tool for analytical and numeric solutions. The results of the present method are compared with those obtained by Adomian Decomposition Method and exact solutions. The results have shown that DTM method has better performs.