Numerical Algorithms

, Volume 60, Issue 3, pp 463–481

An improved spectral homotopy analysis method for MHD flow in a semi-porous channel


  • Sandile Sydney Motsa
    • School of Mathematical SciencesUniversity of KwaZulu-Natal
    • Department of MathematicsUniversity of Venda
  • Gerald T. Marewo
    • Department of MathematicsUniversity of Swaziland
  • Precious Sibanda
    • School of Mathematical SciencesUniversity of KwaZulu-Natal
Original Paper

DOI: 10.1007/s11075-011-9523-0

Cite this article as:
Motsa, S.S., Shateyi, S., Marewo, G.T. et al. Numer Algor (2012) 60: 463. doi:10.1007/s11075-011-9523-0


In this paper we report on a novel method for solving systems of highly nonlinear differential equations by blending two recent semi-numerical techniques; the spectral homotopy analysis method and the successive linearisation method. The hybrid method converges rapidly and is an enhancement of the utility of the original spectral homotopy analysis method (Motsa et al., Commun Nonlinear Sci Numer Simul 15:2293–2302, 2010; Computer & Fluids 39:1219–1225, 2010) and an improvement on other recent semi-analytical techniques. We illustrate the application of the method by solving a system of nonlinear differential equations that govern the problem of laminar viscous flow in a semi-porous channel subject to a transverse magnetic field. A comparison with the numerical solution confirms the validity and accuracy of the technique and shows that the method converges rapidly and gives very accurate results.


Improved spectral homotopy analysis methodCoupled nonlinear equationsLaminar two-dimensional flowElectrically conducting incompressible viscous fluid

Copyright information

© Springer Science+Business Media, LLC. 2011