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Neural Computing and Applications
Erschienen in: Neural Computing and Applications 7-8/2014

01.12.2014 | Original Article

Application of three unsupervised neural network models to singular nonlinear BVP of transformed 2D Bratu equation

verfasst von: Muhammad Asif Zahoor Raja, Raza Samar, Mohammad Mehdi Rashidi

Erschienen in: Neural Computing and Applications | Ausgabe 7-8/2014

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Abstract

In this paper, numerical techniques are developed for solving two-dimensional Bratu equations using different neural network models optimized with the sequential quadratic programming technique. The original two-dimensional problem is transformed into an equivalent singular, nonlinear boundary value problem of ordinary differential equations. Three neural network models are developed for the transformed problem based on unsupervised error using log-sigmoid, radial basis and tan-sigmoid functions. Optimal weights for each model are trained with the help of the sequential quadratic programming algorithm. Three test cases of the equation are solved using the proposed schemes. Statistical analysis based on a large number of independent runs is carried out to validate the models in terms of accuracy, convergence and computational complexity.
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Metadaten
Titel
Application of three unsupervised neural network models to singular nonlinear BVP of transformed 2D Bratu equation
verfasst von
Muhammad Asif Zahoor Raja
Raza Samar
Mohammad Mehdi Rashidi
Publikationsdatum
01.12.2014
Verlag
Springer London
Erschienen in
Neural Computing and Applications / Ausgabe 7-8/2014
Print ISSN: 0941-0643
Elektronische ISSN: 1433-3058
DOI
https://doi.org/10.1007/s00521-014-1641-x

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