The Application of Homotopy Perturbation Method: An Overview

Abstract

As an effective method for solving linear and nonlinear equations, the homotopy perturbation method is usually applied to solving relevant problems. We analyze 74 studies on the application of the homotopy perturbation method and present a comprehensive review of them with the conclusion obtained: (1) Homotopy perturbation method is generally applied to solving the problems of ordinary differential equations; (2) Homotopy perturbation method is usually combined with the technology of transform when it is used to solve more complicated equations; (3) By comparing homotopy perturbation method with other similar methods, many researchers sought that homotopy perturbation method is rapidly convergent, highly accurate, computational simple; (4) Some studies point out that when homotopy perturbation method is applied, some parameters including the number of terms, time span, time step must be prescribed carefully. Finally, two suggestions on the further study of the application of the HPM are provided.

Influence of temperature on the pull-in characteristics of nano-switches considering surface effect

“…Since the nano-switch governing equation, which contains temperature changes and surface effects, is a strongly nonlinear ordinary differential equation, the solution of the control equation is more complicated. In this paper, the homotopy perturbation method [21] is used to approximate the solution of the governing equation.…”