Neural Computing and Applications

, Volume 31, Issue 1, pp 101–115 | Cite as

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

  • Iftikhar AhmadEmail author
  • Abdul Rehman
  • Fayyaz Ahmad
  • Muhammad Asif Zahoor Raja
Original Article


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.


Painlev́e ANN Activation function GA AI 


Compliance with ethical standards

Conflict of interests

There is no conflict of interest among all the authors.


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Copyright information

© The Natural Computing Applications Forum 2017

Authors and Affiliations

  • Iftikhar Ahmad
    • 1
    Email author
  • Abdul Rehman
    • 1
  • Fayyaz Ahmad
    • 2
  • Muhammad Asif Zahoor Raja
    • 3
  1. 1.Department of MathematicsUniversity of GujratGujratPakistan
  2. 2.Department of StatisticsUniversity of GujratGujratPakistan
  3. 3.Department of Electrical EngineeringCIIT AttockAttockPakistan

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