ARA-Homotopy Perturbation Technique with Applications

Authors

Abdelilah K. Sedeeg, Department of Mathematics, Faculty of Education, Holy Quran and Islamic Sciences University, Omdurman, Sudan\\ Department of Mathematics, Faculty of Sciences and Arts-Almikwah, Albaha University, Albaha, Saudi ArabiaFollow
Rania Saadeh, Department of Mathematics, Zarqa University, Zarqa 13110, JordanFollow
Ahmad Qazza, Department of Mathematics, Zarqa University, Zarqa 13110, JordanFollow
Mohammad A. Amleh, Department of Mathematics, Zarqa University, Zarqa 13110, JordanFollow
Mohand M. Abdelrahim, Department of Mathematics, Faculty of Sciences and Arts-Almikwah, Albaha University, Albaha, Saudi Arabia\\ Department of Mathematics, Faculty of Education, Omdurman Islamic University, Omdurman, SudanFollow

Author Country (or Countries)

Jordan

Abstract

In this study, we propose a novel combination method between the ARA integral transform and the homotopy perturbation approach to solve systems of nonlinear partial differential equations. The difficulty arising in solving nonlinear partial differential equations could simply be overcome by using He’s polynomials during the application of the new method. The proposed technique can provide the solutions of the target problems without pre-assumptions or restrictive constrains in addition to avoiding the round-off errors. The efficiency of the new method is illustrated by applying it to solve different examples of systems of nonlinear partial differential equations. We discuss three interesting applications and solve them by the new approach, called ARA-homotopy perturbation method and get exact solutions, also the results are illustrated in figures.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/170504

Recommended Citation

K. Sedeeg, Abdelilah; Saadeh, Rania; Qazza, Ahmad; A. Amleh, Mohammad; and M. Abdelrahim, Mohand (2023) "ARA-Homotopy Perturbation Technique with Applications," Applied Mathematics & Information Sciences: Vol. 17: Iss. 5, Article 4.
DOI: http://dx.doi.org/10.18576/amis/170504
Available at: https://digitalcommons.aaru.edu.jo/amis/vol17/iss5/4