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Numerical treatment for solving one-dimensional Bratu problem using neural networks

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Abstract

In this paper, numerical treatment is presented for the solution of boundary value problems of one-dimensional Bratu-type equations using artificial neural networks. Three types of transfer functions including Log-sigmoid, radial basis, and tan-sigmoid are used in the neural networks’ modeling. The optimum weights for all the three networks are searched with the interior point method. Various test cases of Bratu-type equations have been simulated using the developed models. The accuracy, convergence, and effectiveness of the methods are substantiated by a large number of simulation data for each model by taking enough independent runs.

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Authors and Affiliations

  1. Centre of Computational Intelligence, PO Box 2300, Islamabad, Pakistan

    Muhammad Asif Zahoor Raja

  2. Department of Electrical Engineering, COMSATS Institute of Information Technology, Attock, Pakistan

    Muhammad Asif Zahoor Raja

  3. Department of Electronic Engineering, International Islamic University, Islamabad, Pakistan

    Muhammad Asif Zahoor Raja

  4. Pakistan Institute of Engineering and Applied Science, Nilore, Islamabad, Pakistan

    Siraj-ul-Islam Ahmad

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  1. Muhammad Asif Zahoor Raja
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  2. Siraj-ul-Islam Ahmad
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Correspondence to Muhammad Asif Zahoor Raja.

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Raja, M.A.Z., Ahmad, SuI. Numerical treatment for solving one-dimensional Bratu problem using neural networks. Neural Comput & Applic 24, 549–561 (2014). https://doi.org/10.1007/s00521-012-1261-2

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  • DOI: https://doi.org/10.1007/s00521-012-1261-2

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