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Heuristic computational intelligence approach to solve nonlinear multiple singularity problem of sixth Painlev́e equation

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Abstract

The present study investigate the numerical solution of nonlinear singular system represented with sixth Painlev́e equation by the strength of artificial intelligence using feed-forward artificial neural networks (ANNs) optimized with genetic algorithms (GAs), interior point technique (IPT), sequential quadratic programming (SQP), and their hybrids. The ANN provided a compatible method for finding nature-inspired mathematical model based on unsupervised error for sixth Painlev́e equation and adaptation of weights of these networks is carried out globally by the competency of GA aided with IPT or SQP algorithms. Moreover, a hybrid approach has been adopted for better proposed numerical results. An extensive statistical analysis has been performed through several independent runs of algorithms to validate the accuracy, convergence, and exactness of the proposed scheme.

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Authors and Affiliations

  1. Department of Mathematics, University of Gujrat, Gujrat, Pakistan

    Iftikhar Ahmad & Abdul Rehman

  2. Department of Statistics, University of Gujrat, Gujrat, Pakistan

    Fayyaz Ahmad

  3. Department of Electrical Engineering, CIIT Attock, Attock, Pakistan

    Muhammad Asif Zahoor Raja

Authors
  1. Iftikhar Ahmad
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  2. Abdul Rehman
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  3. Fayyaz Ahmad
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  4. Muhammad Asif Zahoor Raja
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Correspondence to Iftikhar Ahmad.

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Ahmad, I., Rehman, A., Ahmad, F. et al. Heuristic computational intelligence approach to solve nonlinear multiple singularity problem of sixth Painlev́e equation. Neural Comput & Applic 31, 101–115 (2019). https://doi.org/10.1007/s00521-017-2982-z

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  • DOI: https://doi.org/10.1007/s00521-017-2982-z

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