Analytical Investigation of Hyperbolic Equations via He's Methods

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 were introduced to solve nonlinear heat transfer problems in this Letter, one is He's Variational Iteration Method (VIM) and the other is the Homotopy-Perturbation Method (HPM). Nonlinear hyperbolic equations were used as examples to illustrate the simple solution procedures. These methods were useful and practical for solving the nonlinear hyperbolic equation, which is associated with variable initial condition. Comparison of the results has been obtained by both methods with exact solutions reveals that both methods were tremendously effective.