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An innovative fourth-order numerical scheme with error analysis for Lane-Emden-Fowler type systems

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Abstract

In this paper, we develop a novel higher-order compact finite difference scheme for solving systems of Lane-Emden-Fowler type equations. Our method can handle these problems without needing to remove or modify the singularity. To construct the method, initially, we create a uniform mesh within the solution domain and develop a new efficient compact difference scheme. The presented method approximates the derivatives at the boundary nodal points to effectively handle the singularity. Using a matrix analysis approach, we discuss theoretical issues such as consistency, stability, and convergence. The theoretical order of the method is consistent with the numerical convergence rates. To showcase the method’s effectiveness, we apply it to solve various real-life problems from the literature and compare its performance with existing methods. The proposed method provides better numerical approximations than existing methods and offers high-order accuracy using fewer grid points.

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This article does not involve data sharing since no data sets were analyzed or generated during the present study.

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Authors and Affiliations

  1. Department of Mathematics, Birla Institute of Technology Mesra, 835215, Ranchi, India

    Nirupam Sahoo & Randhir Singh

  2. Scientific Computing Group, Universidad de Salamanca, Plaza de la Merced, 37008, Salamanca, Spain

    Higinio Ramos

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  1. Nirupam Sahoo
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  2. Randhir Singh
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  3. Higinio Ramos
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Correspondence to Randhir Singh.

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Sahoo, N., Singh, R. & Ramos, H. An innovative fourth-order numerical scheme with error analysis for Lane-Emden-Fowler type systems. Numer Algor (2024). https://doi.org/10.1007/s11075-024-01882-0

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