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Numerical simulation of Emden–Fowler integral equation with Green’s function type kernel by Gegenbauer-wavelet, Taylor-wavelet and Laguerre-wavelet collocation methods

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  • Shahni, Julee
  • Singh, Randhir

Abstract

In this paper, we consider the Emden–Fowler integral equation with Green’s function type kernel. We propose three computational algorithms based on the Gegenbauer-wavelet, the Taylor-wavelet, and the Laguerre-wavelet to solve such problems. Firstly, we transform the given problems via the collocations technique to the system of algebraic equations, which are then solved by the Newton–Raphson method to get the required numerical solution. We also provide the error bound of the proposed method. To demonstrate the efficiency of the proposed methods, we consider several examples arising in physical models, including real-life problems. The numerical simulations justify the superiority and high performance of the methods, and the obtained results are compared with some other existing schemes. The comparison shows that the proposed method converges faster than other numerical techniques like Haar-wavelets collocation method, advanced Adomian decomposition method, and simplified reproducing kernel method. The numerical tables and graphs show that the accuracy of the proposed method is very high, even for the few collocation points. The L∞ and the L2 errors decrease gradually with an increase in collocation points, and hence, the current method is stable.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:194:y:2022:i:c:p:430-444
    DOI: 10.1016/j.matcom.2021.12.008
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    References listed on IDEAS

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    1. Neslihan Ozdemir & Aydin Secer & Mustafa Bayram, 2019. "The Gegenbauer Wavelets-Based Computational Methods for the Coupled System of Burgers’ Equations with Time-Fractional Derivative," Mathematics, MDPI, vol. 7(6), pages 1-15, May.
    2. Faheem, Mo & Raza, Akmal & Khan, Arshad, 2021. "Collocation methods based on Gegenbauer and Bernoulli wavelets for solving neutral delay differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 180(C), pages 72-92.
    3. Usman, Muhammad & Hamid, Muhammad & Khan, Zafar Hayat & Haq, Rizwan Ul, 2021. "Neuronal dynamics and electrophysiology fractional model: A modified wavelet approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 570(C).
    4. 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.
    5. Karkera, Harinakshi & Katagi, Nagaraj N. & Kudenatti, Ramesh B., 2020. "Analysis of general unified MHD boundary-layer flow of a viscous fluid - a novel numerical approach through wavelets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 168(C), pages 135-154.
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