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Numerical Solution of Lane–Emden Type Equations Using Multilayer Perceptron Neural Network Method

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Abstract

In this paper, we discuss the multi-layer perceptron artificial neural network technique for the solution of homogeneous and non-homogeneous Lane–Emden type differential equations. Our aim is to produce an optimal solution of Lane–Emden equations with less computation using multi-layer perceptron artificial neural network technique, comparatively other numerical techniques. Several test examples have been considered to determine the robustness of the given method. The results obtained prove that the given technique has the capability to develop into an effective approach for solving Lane–Emden type problems with less computation time and memory space.

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Acknowledgements

The authors are grateful to the National Board of Higher Mathematics (NBHM), Government of India for providing financial support to carry out this work through its project sanctioned Order No. 2/48(1)2016 R&D II/6824. We express our sincere thanks to editor in chief, editor and reviewers for their valuable suggestions to revised this manuscript.

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  1. Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, Prayagraj, UP, 211004, India

    Akanksha Verma & Manoj Kumar

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  1. Akanksha Verma
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  2. Manoj Kumar
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Correspondence to Manoj Kumar.

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Verma, A., Kumar, M. Numerical Solution of Lane–Emden Type Equations Using Multilayer Perceptron Neural Network Method. Int. J. Appl. Comput. Math 5, 141 (2019). https://doi.org/10.1007/s40819-019-0728-6

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  • DOI: https://doi.org/10.1007/s40819-019-0728-6

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