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The Least Squares Homotopy Perturbation Method for Systems of Differential Equations with Application to a Blood Flow Model

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  • Mădălina Sofia Paşca

    (Department of Mathematics, Politehnica University Timişoara, 300006 Timişoara, Romania
    Department of Mathematics, West University of Timişoara, 300223 Timişoara, Romania
    These authors contributed equally to this work.)

  • Olivia Bundău

    (Department of Mathematics, Politehnica University Timişoara, 300006 Timişoara, Romania
    These authors contributed equally to this work.)

  • Adina Juratoni

    (Department of Mathematics, Politehnica University Timişoara, 300006 Timişoara, Romania
    These authors contributed equally to this work.)

  • Bogdan Căruntu

    (Department of Mathematics, Politehnica University Timişoara, 300006 Timişoara, Romania
    These authors contributed equally to this work.)

Abstract

In this paper, least squares homotopy perturbation is presented as a straightforward and accurate method to compute approximate analytical solutions for systems of ordinary differential equations. The method is employed to solve a problem related to a laminar flow of a viscous fluid in a semi-porous channel, which may be used to model the blood flow through a blood vessel, taking into account the effects of a magnetic field. The numerical computations show that the method is both easy to use and very accurate compared to the other methods previously used to solve the given problem.

Suggested Citation

  • Mădălina Sofia Paşca & Olivia Bundău & Adina Juratoni & Bogdan Căruntu, 2022. "The Least Squares Homotopy Perturbation Method for Systems of Differential Equations with Application to a Blood Flow Model," Mathematics, MDPI, vol. 10(4), pages 1-14, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:4:p:546-:d:746086
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    References listed on IDEAS

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    1. Zaman, A. & Ali, N. & Sajid, M., 2017. "Numerical simulation of pulsatile flow of blood in a porous-saturated overlapping stenosed artery," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 134(C), pages 1-16.
    2. Ali Rehman & Zabidin Salleh, 2021. "Influence of Marangoni Convection on Magnetohydrodynamic Viscous Dissipation and Heat Transfer on Hybrid Nanofluids in a Rotating System among Two Surfaces," Mathematics, MDPI, vol. 9(18), pages 1-16, September.
    3. Bagh Ali & Rizwan Ali Naqvi & Amir Haider & Dildar Hussain & Sajjad Hussain, 2020. "Finite Element Study of MHD Impacts on the Rotating Flow of Casson Nanofluid with the Double Diffusion Cattaneo—Christov Heat Flux Model," Mathematics, MDPI, vol. 8(9), pages 1-17, September.
    4. He, Ji-Huan, 2005. "Application of homotopy perturbation method to nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 695-700.
    5. Mubashir Qayyum & Imbsat Oscar & Gaetano Luciano, 2021. "Least Square Homotopy Perturbation Method for Ordinary Differential Equations," Journal of Mathematics, Hindawi, vol. 2021, pages 1-16, October.
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    Cited by:

    1. Eva Kaslik & Mihaela Neamţu & Anca Rădulescu, 2022. "Preface to the Special Issue on “Advances in Differential Dynamical Systems with Applications to Economics and Biology”," Mathematics, MDPI, vol. 10(19), pages 1-3, September.
    2. Remus-Daniel Ene & Nicolina Pop & Marioara Lapadat & Luisa Dungan, 2022. "Approximate Closed-Form Solutions for the Maxwell-Bloch Equations via the Optimal Homotopy Asymptotic Method," Mathematics, MDPI, vol. 10(21), pages 1-13, November.

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