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Numerical Solution of Boundary Value Problems Using Artificial Neural Networks and Harmony Search

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Harmony Search Algorithm (ICHSA 2017)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 514))

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Abstract

In this paper, we present an algorithm based on artificial neural networks (ANNs) and harmony search (HS) for the numerical solution of boundary value problems (BVPs), which evolves in most of the science and engineering applications. An approximate trial solution of the BVPs is constructed in terms of ANN in a way that it satisfies the desired boundary conditions of the differential equation (DE) a utomatically. Approximate satisfaction of the trial solution results in an unsupervised error, which is minimized by training ANN using the harmony search algorithm (HSA). A BVP modeling the flow of a stretching surface is considered here as a test problem to validate the accuracy, convergence and effectiveness of the proposed algorithm. The obtained results are compared with the available exact solution also to test the correctness of the algorithm.

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Acknowledgements

This work was supported by a grant from the National Research Foundation (NRF) of Korea, funded by the Korean government (MSIP) under grant number NRF-2016R1A2A1A05005306, and a Brain Korea 21 (BK-21) fellowship from the Ministry of Education of Korea.

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Authors and Affiliations

  1. Department of Civil, Environmental and Architectural Engineering, Korea University, Seoul, 02841, South Korea

    Neha Yadav, Thi Thuy Ngo & Joong Hoon Kim

  2. National Institute of Technology Uttarakhand, Garhwal, Srinagar, India

    Anupam Yadav

Authors
  1. Neha Yadav
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  2. Thi Thuy Ngo
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  3. Anupam Yadav
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  4. Joong Hoon Kim
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Correspondence to Joong Hoon Kim .

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Editors and Affiliations

  1. TECNALIA, University of the Basque Country ‎(UPV/EHU), Basque Center for Applied Mathematics (BCAM‎), Bilbao, Spain

    Javier Del Ser

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Yadav, N., Ngo, T.T., Yadav, A., Kim, J.H. (2017). Numerical Solution of Boundary Value Problems Using Artificial Neural Networks and Harmony Search. In: Del Ser, J. (eds) Harmony Search Algorithm. ICHSA 2017. Advances in Intelligent Systems and Computing, vol 514. Springer, Singapore. https://doi.org/10.1007/978-981-10-3728-3_12

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  • DOI: https://doi.org/10.1007/978-981-10-3728-3_12

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-3727-6

  • Online ISBN: 978-981-10-3728-3

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