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Kyungpook Mathematical Journal 2017; 57(4): 651-665

Published online December 23, 2017 https://doi.org/10.5666/KMJ.2017.57.4.651

Copyright © Kyungpook Mathematical Journal.

Numerical Solutions of Third-Order Boundary Value Problems associated with Draining and Coating Flows

Jishan Ahmed

Department of Mathematics, Faculty of Science and Engineering, University of Barisal,  Bangladesh

Received: February 5, 2015; Revised: November 17, 2015; Accepted: November 16, 2017

Abstract

Some computational fluid dynamics problems concerning the thin films flow of viscous fluid with a free surface and draining or coating fluid-flow problems can be delineated by third-order ordinary differential equations. In this paper, the aim is to introduce the numerical solutions of the boundary value problems of such equations by variational iteration method. In this paper, it is shown that the third-order boundary value problems can be written as a system of integral equations, which can be solved by using the variational iteration method. These solutions are gleaned in terms of convergent series. Numerical examples are given to depict the method and their convergence.

Keywords: Variational iteration method (VIM), Boundary value problems, Draining and coating Flows, Numerical solutions