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

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.