Abstract
An extend of He's homotopy perturbation method (HPM) is used for finding a new approximate and exact solutions of nonlinear difference differential equations arising in mathematical physics.
To illustrate the effectiveness and the advantage of the proposed method, two models of nonlinear difference equations of special interest in physics are chosen, namely, Ablowitz-Ladik lattice equations and Relativistic Toda lattice difference equations. Comparisons are made between the results of the proposed method and exact solutions. The results show that the HPM is a attracted method in solving the differential difference equations (DDEs). The proposed method will become a much more interesting method for solving nonlinear DDEs in science and engineering.