Three iterative methods for solving Jeffery-Hamel flow problem

Authors

  • Majeed A. AL-Jawary Head of Department of Mathematics, College of Education for Pure Sciences / Ibn-AL-Haithem, Baghdad University, Baghdad, Iraq
  • AL-Zahraa J. Abdul Nabi Dept. of Mathematics, College of Education for Pure Science (Ibn AL-Haytham), University of Baghdad, Baghdad, Iraq

Keywords:

Semi-analytical method, Daftardar-Jafari method, Temimi-Ansari method, Banach contraction method, Jeffery-Hamel flow, Analytic solution.

Abstract

In this article, the nonlinear problem of Jeffery-Hamel flow has been solved analytically and numerically by using reliable iterative and numerical methods. The approximate solutions obtained by using the Daftardar-Jafari method namely (DJM), Temimi-Ansari method namely (TAM) and Banach contraction method namely (BCM). The obtained solutions are discussed numerically, in comparison with other numerical solutions obtained from the fourth order Runge-Kutta (RK4), Euler and previous analytic methods available in literature. In addition, the convergence of the proposed methods is given based on the Banach fixed point theorem. The results reveal that the presented methods are reliable, effective and applicable to solve other nonlinear problems. Our computational works have been done by using the computer algebra system MATHEMATICA®10 to evaluate the terms in the iterative processes.

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Published

20-01-2020

Issue

Vol. 47 No. 1 (2020): Kuwait Journal of Science

Section

Mathematics