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On the MHD boundary layer flow with diffusion and chemical reaction over a porous flat plate with suction/blowing: two reliable methods

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Abstract

In this paper, a Lie-group integrator based on \(GL_4(\mathbb {R})\) and the reproducing kernel functions has been constructed to investigate the flow characteristics in an electrically conducting second-grade fluid over a stretching sheet. Accurate initial values can be achieved when the target equation is matched precisely, and then, we can apply the group preserving scheme (GPS) to get a rather accurate results. On the other hand, the reproducing kernel method (RKM) is successfully applied to the underlying equation with convergence analysis. We show exact and approximate solutions by series in the reproducing kernel space. We use a bounded linear operator in the reproducing kernel space to get the solutions by the reproducing kernel method. Comparison of these two methods demonstrates the power and reliability. Finally, effects of magnetic parameter, viscoelastic parameter, stagnation-point flow, and stretching of the sheet parameters are illustrated.

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Notes

  1. Using the truncation rule for the differential equations over the infinite or semi-infinite intervals, we set \(\eta ^f=\eta _\infty \) as the final value of interval \([0,\infty )\).

  2. \(gl_4(\mathbb {R})\) is the Lie algebra associated with the Lie group \(GL_4(\mathbb {R}).\)

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Acknowledgements

The authors would like to thank the referees for the helpful remarks and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, University of Bonab, Bonab, 55517, Iran

    M. S. Hashemi

  2. Department of Mathematics, Art and Science Faculty, Siirt University, 56100, Siirt, Turkey

    A. Akgül

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  1. M. S. Hashemi
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  2. A. Akgül
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Correspondence to M. S. Hashemi.

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Hashemi, M.S., Akgül, A. On the MHD boundary layer flow with diffusion and chemical reaction over a porous flat plate with suction/blowing: two reliable methods. Engineering with Computers 37, 1147–1158 (2021). https://doi.org/10.1007/s00366-019-00876-0

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