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


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Article Info

DATE

2014-12

AUTHORS

Muhammad Asif Zahoor Raja, Raza Samar, Mohammad Mehdi Rashidi

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. More... »

PAGES

1585-1601

References to SciGraph publications

  • 2011-06. A semismooth sequential quadratic programming method for lifted mathematical programs with vanishing constraints in COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS
  • 1979-10. Symmetry and related properties via the maximum principle in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2010-12. A new stochastic approach for solution of Riccati differential equation of fractional order in ANNALS OF MATHEMATICS AND ARTIFICIAL INTELLIGENCE
  • 2010. Evolutionary Computational Intelligence in Solving the Fractional Differential Equations in INTELLIGENT INFORMATION AND DATABASE SYSTEMS
  • 2014-01. A feasible SQP-GS algorithm for nonconvex, nonsmooth constrained optimization in NUMERICAL ALGORITHMS
  • 2014-03. Numerical treatment for solving one-dimensional Bratu problem using neural networks in NEURAL COMPUTING AND APPLICATIONS
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  • 2011-10. Numerical treatment of nonlinear Emden–Fowler equation using stochastic technique in ANNALS OF MATHEMATICS AND ARTIFICIAL INTELLIGENCE
  • 2012-06. Sequential quadratic programming method with a global search strategy on the cutting-stock problem with rotatable polygons in JOURNAL OF INTELLIGENT MANUFACTURING
  • 2013-12. Neural network optimized with evolutionary computing technique for solving the 2-dimensional Bratu problem in NEURAL COMPUTING AND APPLICATIONS
  • 2013. Numerical Treatment for Painlevé Equation I Using Neural Networks and Stochastic Solvers in INNOVATIONS IN INTELLIGENT MACHINES -3
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    http://scigraph.springernature.com/pub.10.1007/s00521-014-1641-x

    DOI

    http://dx.doi.org/10.1007/s00521-014-1641-x

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1053283790


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