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An efficient numerical approach for solving three-point Lane–Emden–Fowler boundary value problem

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  • Shahni, Julee
  • Singh, Randhir
  • Cattani, Carlo

Abstract

For three-point Lane–Emden–Fowler boundary value problems (LEFBVPs), we propose two robust algorithms consisting of Bernstein and shifted Chebyshev polynomials coupled with the collocation technique. The first algorithm uses the Bernstein collocation method with uniform collocation points, while the second is based on the shifted Chebyshev collocation method with roots as its collocation points. In both algorithms, the equivalent integral equations of three-point LEFBVPs are constructed. Then the approximation and collocation approach are used to generate a system of nonlinear equations. Then we implement Newton’s method to solve this system. The current method is different from the traditional method as we do not require to approximate u′ and u′′ appearing in the problem. It reduces not only the computational time but also the truncation error. The existence of a unique solution is discussed. Error analysis of both algorithms is demonstrated. A well known property of the proposed techniques is that it provides efficient solution for a few collocation points. The numerical results verify the same.

Suggested Citation

  • Shahni, Julee & Singh, Randhir & Cattani, Carlo, 2023. "An efficient numerical approach for solving three-point Lane–Emden–Fowler boundary value problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 210(C), pages 1-16.
    • Handle: RePEc:eee:matcom:v:210:y:2023:i:c:p:1-16
    DOI: 10.1016/j.matcom.2023.03.009
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    References listed on IDEAS

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    1. Singh, Randhir & Guleria, Vandana & Singh, Mehakpreet, 2020. "Haar wavelet quasilinearization method for numerical solution of Emden–Fowler type equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 174(C), pages 123-133.
    2. Mohsen Alipour & Dumitru Baleanu & Fereshteh Babaei, 2014. "Hybrid Bernstein Block-Pulse Functions Method for Second Kind Integral Equations with Convergence Analysis," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-8, February.
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