Analysis of various semi-numerical schemes for magnetohydrodynamic (MHD) squeezing fluid flow in porous medium

Inayat Ullah ^a,*, M.T. Rahim ^b, Hamid Khan ^b, Mubashir Qayyum ^b

a. Department of Mathematics, Edwardes College Peshawar, Khyber Pakhtunkhwa (KPK) 25000, Pakistan
         b. Department of Humanities, FAST NUCES Peshawar Campus, Khyber Pakhtunkhwa (KPK) 25000, Pakistan

Abstract: In this article comparative analysis of various semi-numerical schemes has been made for the case of squeezing flow of an incompressible viscous fluid between two large parallel plates having no-slip at the boundaries. The medium of flow contains magnetohydrodynamic (MHD) effect and having small pores. Modeled boundary value problem is solved analytically using Optimal homotopy asymptotic method (OHAM), homotopy perturbation method (HPM), differential transform method (DTM), Daftardar Jafari method (DJM) and adomian decomposition method (ADM). For comparison purpose, residuals of these schemes have been found and analyzed for accuracy. Analytical study indicates that DTM and DJM are quite good in term of accuracy near the center of domain [-1, 1] but the accuracy reduces considerably near the start and end of the given interval. HPM and OHAM residuals indicate that OHAM surpasses HPM in terms of accuracy in the present case.

Keywords: Optimal homotopy asymptotic method; Homotopy perturbation method; Differential transform method; Daftardar Jafari method; Adomian decomposition method