Theoretical analysis of new techniques applied to applications in fluid dynamics

ABSTRACTIn this research study, we explore new proofs of theorems related to a novel technique by the name of the natural Adomian decomposition method (NADM), and then we apply it to find new exact solutions to nonlinear partial differential equations under proper initial conditions. Our solutions to nonlinear differential equations are given in series format, with convergence analysis for the proposed scheme. The new approach in this work can be considered as an alternative technique for the ones in the literature, to handle KdV-type equations such as the fifth-order Korteweg–de Vries (efKdV) equation, which is a crucial equation in fluid dynamics for the description of nonlinear wave processes. The new technique is a novel one to treat applications in the fields of mathematics, biology, engineering, physics, and other areas of science.KEYWORDS: Fluid dynamicsnatural transformAdomian decomposition methodpartial differential equationfixed point theory AcknowledgmentsThe authors appreciate the constructive criticism and recommendations from the anonymous referees, which helped raise the paper’s caliber.Disclosure statementNo potential conflict of interest was reported by the author(s).Data availability statementData sharing is not applicable to this article as no data sets were generated or analyzed during the current study.Consent to participateParticipants are aware that they can contact the University of Vermont Ethics Officer if they have any concerns or complaints regarding the way in which the research is or has been conducted.Additional informationFundingNo funding was provided for this research.Notes on contributorsNazek A. ObeidatNazek Obeidat received her undergraduate degree in mathematics from the University of Findlay (USA) in 2008, graduating with summa cum laude. She received her M.Sc. in Mathematics from the University of Toledo in 2020, and she received her PHD from the University of Vermont in 2022. She was recognized for excellent academic achievement and made the Dean’s List for 2004 and 2005 at the University of Toledo and recognized for excellent academic achievement and made the Dean’s List in 2006, 2007, and 2008 at the University of Findlay Currently, she is a postdoctoral researcher, and she has published many articles in highly respected journals. Finally, she is a referee in a highly respected international mathematical journal.Mahmoud S. RawashdehMahmoud Rawashdeh joined the Department of Mathematics and Statistics at Jordan University of Science and Technology (Jordan) in 2009. Prior to coming to the Faculty of Science and Arts at (JUST), he was a tenured assistant professor at the University of Findlay (USA) (2006–2009). He received his undergraduate degree in Mathematics from Yarmouk University (Jordan) in 1989. He received his M.A in Mathematics from City University of New York, New York, USA in June 1997 and his Ph.D. in Applied Mathematics from The University of Toledo, Ohio, USA in May 2006. His research interest include topics in the areas of Applied Mathematics, such as; tempered fractional calculus and mathematical modelling applications in the area of science. His research involves using numerical iterative methods to obtain approximate and exact solutions to fractional partial differential equations arising from nonlinear PDEs problems in engineering and Physics. He has published research articles in a well-recognized international journal of mathematical and engineering sciences. He is a referee in a highly respected mathematical journals.