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An Efficient Method for Solving the Generalized Thomas–Fermi and Lane–Emden–Fowler Type Equations with Nonlocal Integral Type Boundary Conditions

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Abstract

In this work, we examine various physical phenomena modeled by nonclassical boundary value problems with nonlocal boundary conditions. We concern our analysis on a new type of nonlocal boundary value problems, i.e., the semi-numerical solution of the generalized Thomas–Fermi type equations and Lane–Emden–Fowle type equations subjected to integral type boundary conditions. We first transform the given nonlocal boundary value problems into equivalent integral equations, followed by applying a modified decomposition method, which facilitates computational work. Moreover, we show that the proposed scheme is convergent in a suitable Banach space. A sufficient theorem is supplied for the uniqueness of the solution of the problems. The proposed method approximates the solution in series with easily computable components without restrictive assumptions such as linearization, discretization, and perturbation. Several examples are included to show the accuracy, applicability, and overview of the method.

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Authors and Affiliations

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

    Randhir Singh

  2. Department of Mathematics, Saint Xavier University, Chicago, IL, 60655, USA

    Abdul-Majid Wazwaz

Authors
  1. Randhir Singh
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  2. Abdul-Majid Wazwaz
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Contributions

RS contributed to formulation, methodology and programming. A-MW contributed to formulation. Both authors contributed equally in writing the paper and both read and approved the final manuscript.

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Singh, R., Wazwaz, AM. An Efficient Method for Solving the Generalized Thomas–Fermi and Lane–Emden–Fowler Type Equations with Nonlocal Integral Type Boundary Conditions. Int. J. Appl. Comput. Math 8, 68 (2022). https://doi.org/10.1007/s40819-022-01280-x

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