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Single Layer Chebyshev Neural Network Model for Solving Elliptic Partial Differential Equations

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Abstract

The purpose of the present study is to solve partial differential equations (PDEs) using single layer functional link artificial neural network method. Numerical solution of elliptic PDEs have been obtained here by applying Chebyshev neural network (ChNN) model for the first time. Computations become efficient because the hidden layer is eliminated by expanding the input pattern by Chebyshev polynomials. Feed forward neural network model with unsupervised error back propagation principle is used for modifying the network parameters and to minimize the computed error function. Numerical efficiency and accuracy of the ChNN model are investigated by three test problems of elliptic partial differential equations. The results obtained by this method are compared with the existing methods and are found to be in good agreement.

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Acknowledgments

The first author would like to acknowledge the Department of Science and Technology (DST), Government of India for financial support under Women Scientist Scheme-A. Also the authors would like to thank Editor in chief and the Reviewers for their valuable suggestions to improve this work.

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology Rourkela, Odisha, 769008, India

    Susmita Mall & S. Chakraverty

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  1. Susmita Mall
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  2. S. Chakraverty
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Correspondence to S. Chakraverty.

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Mall, S., Chakraverty, S. Single Layer Chebyshev Neural Network Model for Solving Elliptic Partial Differential Equations. Neural Process Lett 45, 825–840 (2017). https://doi.org/10.1007/s11063-016-9551-9

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  • DOI: https://doi.org/10.1007/s11063-016-9551-9

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