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

Pinky M Shah; Jyotindra C Prajapati

doi:10.48165/

Authors

Pinky M Shah Department of Mathematics, Veer Narmad South Gujarat University, Surat, Gujarat-365005, India.
Jyotindra C Prajapati Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar, Anand, Gujarat-388120, India.

DOI:

https://doi.org/10.48165/

Keywords:

Squeezing flow, Non-linear equation, Spline collocation method, Quasilin earization technique, Homotopy perturbation method

Abstract

An analysis is carried out in this paper to study two-dimensional and axisym metric 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 (Bick ley (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 ho motopy perturbration method (HPM) and the Runge-Kutta fourth order method. The physical interpretation is discussed and the results are demonstrated graphically.

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