Approximation solution of the squeezing flow by the modification of optimal homotopy asymptotic method
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Approximation solution of the squeezing flow by the modification of optimal homotopy asymptotic method a ˙ Onur Alp Ilhan
Department of Mathematics, Faculty of Education, Erciyes University, 38039 Melikgazi, Kayseri, Turkey Received: 22 July 2020 / Accepted: 26 August 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The approximate solution of the squeezing axisymmetric fluid flow between infinite plates is discussed in the present paper. An optimal homotopy analysis method with a modification function technique is proposed to solve a class of nonlocal boundary value problems, namely squeezing axisymmetric fluid flow equation. We first transform the nonlocal boundary value problems into an equivalent integral equation, and then the optimal homotopy analysis technique is utilized for an approximate solution. The numerical results confirm the reliability of the present method as it tackles such nonlocal problems without any limiting assumptions. The proposed method is tested upon squeezing axisymmetric fluid flow equation from the literature and the results are compared with the available approximate solutions including perturbation method (Ran et al. in Commun Nonlinear Sci Numer Simul, 2007. https://doi.org/10.1016/j.cnsns), homotopy perturbation method (Ran et al. 2007), homotopy analysis method (Ran et al. 2007), and optimal homotopy asymptotic method (Idrees et al. in Math Comput Model 55:1324–1333, 2012). The convergence and error analysis of the proposed method is discussed. It can be said that squeezing the axisymmetric fluid flow equation exists in different dynamical behaviors. In addition, the physical behaviors of these new exact solutions are given with two and three-dimensional graphs.
1 Introduction Nonlinear partial differential equations play an important role in modeling numerous important phenomena occurring in various fields of physics and engineering sciences, which are frequently modeled through nonlinear partial differential equations [1]. The mathematical models describing the Newtonian fluids are easy to solve as compared to the mathematical models of non-Newtonian fluids [2–4]. Squeezing flows are induced by externally implemented normal stresses or vertical velocities by help of a mobile boundary [1]. Different applications of squeezing flows appear in food industry, chemical engineering, polymer processing, compression, injection modeling and lubrication systems, one can express that squeezing flows have been widely received considerable attention due to the practical applications in physical and biophysical areas [5–8]. Ran et al. [7] made comparison between HAM and numerical method for squeezing flow between two parallel plates. Lubrication approximation technique for solving the squeezing flow was studied by Stefan [9]. Applica-
a e-mail: [email protected] (corresponding author)
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tions of the squeezing flow for obtaining solutions of ellip
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