He–Laplace method for nonlinear vibration systems and nonlinear wave equations

Abstract

This study suggests a new approach for solving telegraph equation, commonly called damped wave equation, arising in electromagnetic waves and propagation of electrical signals. In this paper, He–Laplace method, formulated by He’s variational iteration method and Laplace transformation, is used to find the exact solution or a closed approximate solution of differential equations. The most distinct aspect of this method is that there is no need to calculate integration for next iterations in recurrence relations and convolution theorem is kept away to calculate the Lagrange multipliers in Laplace transformation. Moreover, He’s polynomials via homotopy perturbation method is introduced to bring down the computational work in nonlinear terms as Laplace transform has some limitation to nonlinear terms. The results obtained by proposed method indicate that this approach is easy to implement and converges rapidly to exact solution. Several problems are illustrated to demonstrate the accuracy and stability of this method.