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Haar wavelet quasilinearization method for numerical solution of Emden–Fowler type equations

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  • Singh, Randhir
  • Guleria, Vandana
  • Singh, Mehakpreet

Abstract

In this paper, an efficient method for solving the nonlinear Emden–Fowler type boundary value problems with Dirichlet and Robin–Neumann boundary conditions is introduced. The present method is based on the Haar-wavelets and quasilinearization technique. The quasilinearization technique is adopted to linearize the nonlinear singular problem. Numerical solution of linear singular problem is obtained by the Haar wavelet method. The numerical study is further supported by examining thoroughly the convergence of the Haar wavelet method and the quasilinearization technique. In order to check the accuracy of the proposed method, the numerical results are compared with both existing methods and exact solutions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:174:y:2020:i:c:p:123-133
    DOI: 10.1016/j.matcom.2020.02.004
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    References listed on IDEAS

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    1. Lepik, Ü., 2005. "Numerical solution of differential equations using Haar wavelets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 68(2), pages 127-143.
    2. Hsiao, Chun-Hui & Wang, Wen-June, 2001. "Haar wavelet approach to nonlinear stiff systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 57(6), pages 347-353.
    3. Hsiao, C.H., 2004. "Haar wavelet approach to linear stiff systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 64(5), pages 561-567.
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    Citations

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    Cited by:

    1. Sriwastav, Nikhil & Barnwal, Amit K. & Ramos, Higinio & Agarwal, Ravi P. & Singh, Mehakpreet, 2024. "Advanced numerical scheme and its convergence analysis for a class of two-point singular boundary value problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 216(C), pages 30-48.
    2. 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.
    3. Vikash Kumar Sinha & Prashanth Maroju, 2023. "New Development of Variational Iteration Method Using Quasilinearization Method for Solving Nonlinear Problems," Mathematics, MDPI, vol. 11(4), pages 1-11, February.
    4. Zare, Farideh & Heydari, Mohammad & Loghmani, Ghasem Barid, 2024. "Convergence analysis of an iterative scheme to solve a family of functional Volterra integral equations," Applied Mathematics and Computation, Elsevier, vol. 477(C).
    5. Tomar, Saurabh & Dhama, Soniya & Ramos, Higinio & Singh, Mehakpreet, 2023. "An efficient technique based on Green’s function for solving two-point boundary value problems and its convergence analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 210(C), pages 408-423.
    6. Ramos, Higinio & Rufai, Mufutau Ajani, 2022. "An adaptive pair of one-step hybrid block Nyström methods for singular initial-value problems of Lane–Emden–Fowler type," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 497-508.
    7. Swati, & Singh, Mandeep & Singh, Karanjeet, 2023. "An efficient technique based on higher order Haar wavelet method for Lane–Emden equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 21-39.
    8. Shahni, Julee & Singh, Randhir, 2022. "Numerical simulation of Emden–Fowler integral equation with Green’s function type kernel by Gegenbauer-wavelet, Taylor-wavelet and Laguerre-wavelet collocation methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 430-444.

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