New applications of He's homotopy perturbation method for nonlinear differential difference equations

Abstract

We extend He's homotopy perturbation method (HPM) with a computerized symbolic computation to find approximate and exact solutions for nonlinear differential difference equations (DDEs) arising in physics. The results reveal that the method is very effective and simple. We find that the extended method for nonlinear DDEs is of good accuracy. To illustrate the effectiveness and the advantage of the proposed method, three models of nonlinear DDEs of special interest in physics are chosen, namely, the hybrid equation, the Toda lattice equation and the relativistic Toda lattice difference equation. Comparisons are made between the results of the proposed method and exact solutions. The results show that the HPM is an attractive method for solving the DDEs.