APPLICATION OF THE VARIATIONAL ITERATION METHOD AND THE HOMOTOPY PERTURBATION METHOD TO HYPERBOLIC EQUATIONS

M. Hassanzadeh (Iran), D. D. Ganji (Iran), F. Ahangarian (Iran) and A. Kolahdooz (Iran)

Received December 19, 2007

Abstract

Perturbation methods depend on a small parameter which is difficult to be found for real-life nonlinear problems. To overcome this shortcoming, two new but powerful analytical methods are introduced to solve nonlinear heat transfer problems in this paper; one is He’s variational iteration method (VIM) and the other is the homotopy perturbation method (HPM). Nonlinear hyperbolic equations are used as examples to illustrate the simple solution procedures. These methods are useful and practical for solving the nonlinear hyperbolic equation, which is associated with variable initial condition. Comparison of the results obtained by both methods with exact solutions reveals that both methods are tremendously effective.

Keywords and phrases: hyperbolic equations, homotopy perturbation method, variation iteration method.