Restarted Shooting Method Applied to Jeffery-Hamel Flow Problem

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DOI: https://doi.org/10.28924/2291-8639-23-2025-17
Published: Jan 20, 2025
Cite as:
Nawal Alzaid, Kholoud Alzahrani, Huda Bakodah, Restarted Shooting Method Applied to Jeffery-Hamel Flow Problem, Int. J. Anal. Appl., 23 (2025), 17.

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Nawal Alzaid, Kholoud Alzahrani, Huda Bakodah

Abstract

In the current manuscript, an efficient numerical method based on coupling the restarted decomposition method and the shooting method has been implemented to tackle the nonlinear differential equation that describes blood flow in human arteries. A complete outline of the coupled method has been provided and further utilized on the generalized Jeffery-Hamel blood flow problem. In addition, the acquired computational results are contrasted with the numerical results of other computational approaches. Lastly, the efficacy of the devised numerical method is confirmed by the maximum error remainder and is reported through comparison tables and figures.

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References

  1. I. Ahmad, H. Ilyas, Homotopy Perturbation Method for the Nonlinear MHD Jeffery–Hamel Blood Flows Problem, Appl. Numer. Math. 141 (2019), 124–132. https://doi.org/10.1016/j.apnum.2018.07.005.
  2. G.B. Jeffery, L. The Two-Dimensional Steady Motion of a Viscous Fluid, Phil. Mag. 29 (1915), 455–465. https://doi.org/10.1080/14786440408635327.
  3. G. Hamel, Spiralförmige Bewegungen Zäher Flüssigkeiten, Jahresber. Dtsch. Math.-Ver. 25 (1917), 34–60. http://eudml.org/doc/145468.
  4. J.H. He, A Review on Some New Recently Developed Nonlinear Analytical Techniques, Int. J. Nonlinear Sci. Numer. Simul. 1 (2000), 51–70. https://doi.org/10.1515/IJNSNS.2000.1.1.51.
  5. J.H. He, Homotopy Perturbation Method for Bifurcation of Nonlinear Problems, Int. J. Nonlinear Sci. Numer. Simul. 6 (2005), 207–208. https://doi.org/10.1515/IJNSNS.2005.6.2.207.
  6. J.K. Zhou, Differential Transformation and Its Applications for Electrical Circuits, Huazhong University Press, Wuhan, China, 1986.
  7. G. Adomian, Nonlinear Stochastic Systems Theory and Applications to Physics, Kluwer Academic Publishers, Dordrecht, 1989.
  8. G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Publishers, Boston, MA, 1994.
  9. K. Abbaoui, Y. Cherruault, Convergence of Adomian’s Method Applied to Nonlinear Equations, Math. Comput. Model. 20 (1994), 69–73. https://doi.org/10.1016/0895-7177(94)00163-4.
  10. E. Babolian, S. Javadi, Restarted Adomian Method for Algebraic Equations, Appl. Math. Comput. 146 (2003), 533–541. https://doi.org/10.1016/S0096-3003(02)00603-3.
  11. H. Sadeghi Goghary, Sh. Javadi, E. Babolian, Restarted Adomian Method for System of Nonlinear Volterra Integral Equations, Appl. Math. Comput. 161 (2005), 745–751. https://doi.org/10.1016/j.amc.2003.12.072.
  12. I.U. Rahman, M. Sulaiman, F.K. Alarfaj, P. Kumam, G. Laouini, Investigation of Non-Linear MHD Jeffery–Hamel Blood Flow Model Using a Hybrid Metaheuristic Approach, IEEE Access 9 (2021), 163214–163232. https://doi.org/10.1109/ACCESS.2021.3133815.
  13. A.S. Bataineh, O.R. Isik, I. Hashim, Bernstein Collocation Method for Solving MHD Jeffery–Hamel Blood Flow Problem with Error Estimations, Int. J. Differ. Equ. 2022 (2022), 9123178. https://doi.org/10.1155/2022/9123178.
  14. A.A. Joneidi, G. Domairry, M. Babaelahi, Three Analytical Methods Applied to Jeffery–Hamel Flow, Commun. Nonlinear Sci. Numer. Simul. 15 (2010), 3423–3434. https://doi.org/10.1016/j.cnsns.2009.12.023.
  15. G. Adomian, Solutions of Nonlinear P.D.E., Appl. Math. Lett. 11 (1998), 121–123. https://doi.org/10.1016/S0893-9659(98)00043-3.
  16. M. N’Dour, Y. Cherruault, The Decomposition Method Applied to a Diffusion Model, Kybernetes 26 (1997), 921–935. https://doi.org/10.1108/03684929710367528.
  17. E. Babolian, H.S. Goghary, Sh. Javadi, M. Ghasemi, Restarted Adomian Method for Nonlinear Differential Equations, Int. J. Comput. Math. 82 (2005), 97–102. https://doi.org/10.1080/00207160412331291071.
  18. A.-M. Wazwaz, A Reliable Modification of Adomian Decomposition Method, Appl. Math. Comput. 102 (1999), 77–86. https://doi.org/10.1016/S0096-3003(98)10024-3.
  19. K.A. Alzahrani, N.A. Alzaid, H.O. Bakodah, M.H. Almazmumy, Computational Approach to Third-Order Nonlinear Boundary Value Problems via Efficient Decomposition Shooting Method, Axioms 13 (2024), 248. https://doi.org/10.3390/axioms13040248.