A Numerical Approach for the Analytical Solution of the Fourth-Order Parabolic Partial Differential Equations. (16th August 2022)

• Record Type: Journal Article
• Authors: Liu, Fenglian; Nadeem, Muhammad; Mahariq, Ibrahim; Dawood, Suliman
• Other Names: Gurefe Yusuf Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2022(2022)
• Publication Date: 2022-08-16
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2022/3309674
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : In this study, we propose a new iterative scheme (NIS) to investigate the approximate solution of the fourth-order parabolic partial differential equations (PDEs) that arises in transverse vibration problems. We introduce the Mohand transform as a new operator that is very easy to implement coupled with the homotopy perturbation method. This NIS is capable of reducing the linearization, perturbation, and restrictive assumptions that ruin the nature of the numerical problems. Some numerical examples are demonstrated to legitimate the accuracy and authenticity of this NIS. The computational results are obtained in the shape of a series that converges only after a few iterations. The comparison of the graphical representations shows that NIS is a very simple but also an effective approach for other numerical problems involving complex variables.