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

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Abstract

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.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of KwaZulu-Natal, Private Bag X01, Scottsville, Pietermaritzburg, 3209, Republic of South Africa

    Sandile Sydney Motsa & Precious Sibanda

  2. Department of Mathematics, University of Venda, Private Bag X5050, Thohoyandou, 0950, Republic of South Africa

    Stanford Shateyi

  3. Department of Mathematics, University of Swaziland, Private Bag 4, Kwaluseni, Swaziland

    Gerald T. Marewo

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  1. Sandile Sydney Motsa
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  2. Stanford Shateyi
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  3. Gerald T. Marewo
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  4. Precious Sibanda
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Correspondence to Stanford Shateyi.

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Motsa, S.S., Shateyi, S., Marewo, G.T. et al. An improved spectral homotopy analysis method for MHD flow in a semi-porous channel. Numer Algor 60, 463–481 (2012). https://doi.org/10.1007/s11075-011-9523-0

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