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Stochastic numerical treatment for solving Falkner–Skan equations using feedforward neural networks

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Abstract

In this article, the artificial intelligence techniques have been used for the solution of Falkner–Skan (FS) equations based on neural networks optimized with three methods including active set technique, sequential quadratic programming and genetic algorithms (GA) hybridization. Log-sigmoid activation function is used in artificial neural network architecture. The proposed techniques are applied to a number of cases for Falkner–Skan problems, and results were compared with GA hybrid results in all cases and were found accurate. The level of accuracy is examined through statistical analyses based on a sufficiently large number of independent runs.

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Acknowledgments

The authors would like to thank Dr. Muhammad Asif Zahoor Raja for help in this research work.

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Authors and Affiliations

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

    Iftikhar Ahmad & Nabeela Anwar

  2. Research in Simulation and Modeling (RIMS), Department of Physics, CIIT, Park Road, Islamabad, Pakistan

    Siraj-ul-Islam Ahmad

  3. Department of Mathematics, University of Malaysia Pahang, Pekan, Malaysia

    Muhammad Bilal

Authors
  1. Iftikhar Ahmad
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  2. Siraj-ul-Islam Ahmad
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  3. Muhammad Bilal
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  4. Nabeela Anwar
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Correspondence to Iftikhar Ahmad.

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Ahmad, I., Ahmad, SuI., Bilal, M. et al. Stochastic numerical treatment for solving Falkner–Skan equations using feedforward neural networks. Neural Comput & Applic 28 (Suppl 1), 1131–1144 (2017). https://doi.org/10.1007/s00521-016-2427-0

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  • DOI: https://doi.org/10.1007/s00521-016-2427-0

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