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Bulletin of Pure and Applied Sciences- Math& Stat. (Started in 1982)
eISSN: 2320-3226
pISSN: 0970-6577
Impact Factor: 4.895 (2017)
DOI: 10.5958/2320-3226
Editor-in-Chief:  Prof. Dr. Lalit Mohan Upadhyaya
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Article Details

Bulletin of Pure and Applied Sciences- Math& Stat. (Started in 1982)
Year : 2019, Volume & Issue : BPAS-Maths & Stat 38E(2), JUL-DEC 2019
Page No. : 525-531, Article Type : Original Aticle
Article DOI : 10.5958/2320-3226.2019.00053.5 (Communicated, edited and typeset in Latex by Lalit Mohan Upadhyaya (Editor-in-Chief). Received December 28, 2018 / Revised April 12, 2019 / Accepted May 18, 2019. Online First Published on December 24, 2019 )

Spline collocation approach to study two-dimensional and axisymmetric unsteady flow

Pinky M. Shah1 and Jyotindra C. Prajapati2
Author’s Affiliation : 1. Department of Mathematics, Veer Narmad South Gujarat University, Surat, Gujarat-365005, India. 2. Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar, Anand, Gujarat-388120, India. 1. E-mail: [email protected] , 2. E-mail: [email protected]

Corresponding Author : Jyotindra C. Prajapati,
E-Mail:-[email protected]


Abstract

An analysis is carried out in this paper to study two-dimensional and axisymmetric  flow of a viscous incompressible fluid between two parallel plates. The governing non-linear equation of the flow problem is transformed into a linear differential equation using quasilinearization technique (Bellman and Kalaba (1965), Quasilinearization and non-linear boundary value problems, American Elsevier Publishing Company Inc., New York.) and quintic spline collocation method is applied to solve the linear problem (Bickley (1968), Piecewise cubic interpolation and two-point boundary value problems, Comp. J., 11, 206–208). The numerical results obtained by this method are compared with homotopy perturbration method (HPM) and the Runge-Kutta fourth order method. The physical interpretation is discussed and the results are demonstrated graphically.

2010 Mathematics Subject Classification: Primary: 34B15, 34G20, 41A15.

Keywords

Squeezing flow, Non-linear equation, Spline collocation method, Quasilinearization technique, Homotopy perturbation method.
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