A new modification of the homotopy perturbation method. (July 2021)

• Record Type: Journal Article
• Authors: Yunbunga Adamu, Magaji; Ogenyi, Peter
• Is Part Of: Noise & vibration worldwide. Volume 52:Number 7/8(2021)
• Page Start: 191
• Page End: 199
• Publication Date: 2021-07
• Subjects: Homotopy perturbation method -- homotopy equation -- nonlinear oscillator -- alpha parameter -- Duffing oscillator -- Van der Pol oscillator; Noise control -- Periodicals; Damping (Mechanics) -- Periodicals; Soundproofing -- Periodicals; Damping (Mechanics); Noise control; Soundproofing; Periodicals; 620.205
• DOI: 10.1177/0957456521999875
• Languages: English
• ISSNs: 0957-4565

Abstract

This study proposes a new modification of the homotopy perturbation method. A new parameter alpha is introduced into the homotopy equation in order to improve the results and accuracy. An optimal analysis identifies the parameter alpha, aimed at improving the solutions. A comparative analysis of the proposed method reveals that the new method presents results with higher degree of accuracy and precision than the classic homotopy perturbation method. Absolute error analysis shows the convenience of the proposed method, providing much smaller errors. Two examples are presented: Duffing and Van der pol's nonlinear oscillators to demonstrate the efficiency, accuracy, and applicability of the new method.