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Numerical solution of coupled Lane–Emden–Fowler type equation by embedded quasilinearization method with homotopy analysis method

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  • Vikash Kumar Sinha

    (VIT AP University)

  • Prashanth Maroju

    (VIT AP University)

Abstract

This paper aims to study the solution of coupled Emden-Folwer type equations by embedding the quasilinearization algorithm enclosed by the homotopy analysis method. This approach is easy to implement and converges to a solution very fast. The convergence analysis of our method is discussed in Banach space. Some numerical examples are taken to verify the validity, accuracy as well as generality of our proposed method. We calculate the approximate analytic solutions and compare them with the Duan’s Adomian decomposition method [2] and Singh et. al [6]. We observe that our approach gives better accuracy than the existing ADM and equally compete with Singh et. al.

Suggested Citation

  • Vikash Kumar Sinha & Prashanth Maroju, 2025. "Numerical solution of coupled Lane–Emden–Fowler type equation by embedded quasilinearization method with homotopy analysis method," Indian Journal of Pure and Applied Mathematics, Springer, vol. 56(1), pages 230-240, March.
    • Handle: RePEc:spr:indpam:v:56:y:2025:i:1:d:10.1007_s13226-023-00475-2
    DOI: 10.1007/s13226-023-00475-2
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    References listed on IDEAS

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    1. Sandile S. Motsa & Precious Sibanda, 2013. "On Extending the Quasilinearization Method to Higher Order Convergent Hybrid Schemes Using the Spectral Homotopy Analysis Method," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-9, April.
    2. Eman S. Alaidarous & Malik Zaka Ullah & Fayyaz Ahmad & A.S. Al-Fhaid, 2013. "An Efficient Higher‐Order Quasilinearization Method for Solving Nonlinear BVPs," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    3. Eman S. Alaidarous & Malik Zaka Ullah & Fayyaz Ahmad & A.S. Al-Fhaid, 2013. "An Efficient Higher-Order Quasilinearization Method for Solving Nonlinear BVPs," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-11, November.
    4. Sandile S. Motsa & Precious Sibanda, 2013. "On Extending the Quasilinearization Method to Higher Order Convergent Hybrid Schemes Using the Spectral Homotopy Analysis Method," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    5. Tomar, Saurabh & Singh, Mehakpreet & Vajravelu, Kuppalapalle & Ramos, Higinio, 2023. "Simplifying the variational iteration method: A new approach to obtain the Lagrange multiplier," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 640-644.
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