Applications of He's Homotopy Perturbation Method to Obtain Second-order Approximations of the Coupled Two-Degree-of-Freedom Systems

✍ Scribed by Ganji, S. S.; Ganji, D. D.; Karimpour, S.; Babazadeh, H.

• Book ID: 120609552
• Publisher: Walter de Gruyter GmbH & Co. KG
• Year: 2009
• Tongue: English
• Weight: 809 KB
• Volume: 10
• Category: Article
• ISSN: 1565-1339
• DOI: 10.1515/IJNSNS.2009.10.3.305

✦ Synopsis

In this paper we apply a Modified He's Homotopy Perturbation Method (MHHPM) as a strong method to solve accurately higher-order approximate analytical solutions of coupled two-degree-of-freedom (CTDOF), which is described with a system of two coupled strong non-linear differential equations. MHHPM is modified version of He's HPM by truncating the infinite series corresponding to the first-order approximate solution before introducing this solution into the second-order linear differential equation. For the first approximation we achieve a high accuracy of solutions with a maximal relative error less than 3.14 % for small and large values of oscillation amplitude, while for the second iteration the fabulous relative error is 0.064 %. It is predicted that MHHPM can be found widely applicable in engineering which needs extremely accurate solutions.