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Numerical Solution of a Class of Singular Boundary Value Problems Arising in Physiology Based on Neural Networks

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Proceedings of Fifth International Conference on Soft Computing for Problem Solving

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 437))

Abstract

In this paper, a soft computing approach based on neural networks is presented for the numerical solution of a class of singular boundary value problems (SBVP) arising in physiology. The mathematical model of artificial neural network (ANN) is developed in a way to satisfy the boundary conditions exactly using log-sigmoid activation function in hidden layers. Training of the neural network parameters was performed by gradient descent backpropagation algorithm with sufficient number of independent runs. Two test problems from physical applications have been considered to check the accuracy and efficiency of the method. Proposed results for the solution of SBVP have been compared with the exact analytical solution as well as the solution obtained by the existing numerical methods and shows good agreement with others.

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Acknowledgments

This work was supported by National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIP) (NRF-2013R1A2A1A01013886) and the Brain Korea 21 (BK-21) fellowship from the Ministry of Education of Korea.

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Authors and Affiliations

  1. School of Civil, Environmental and Architectural Engineering, Korea University, Seoul, 136-713, South Korea

    Neha Yadav & Joong Hoon Kim

  2. Department of Sciences and Humanities, National Institute of Technology, Uttarakhand, Srinagar, 246174, Uttarakhand, India

    Anupam Yadav

Authors
  1. Neha Yadav
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  2. Joong Hoon Kim
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  3. Anupam Yadav
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Corresponding author

Correspondence to Joong Hoon Kim .

Editor information

Editors and Affiliations

  1. Dept of Applied Sci & Eng, Indian Instit of Tech Roorkee, Roorkee, India

    Millie Pant

  2. Department of Mathematics, Indian Inst of Tech Roorkee, Roorkee, India

    Kusum Deep

  3. Dept of Mathematics, South Asian University New Delhi, New Delhi, India

    Jagdish Chand Bansal

  4. Department of Mathematics and Comp Sci, Liverpool Hope University, LIVERPOOL, United Kingdom

    Atulya Nagar

  5. Department of Mathematics, National Inst of Tech Silchar, Silchar, Assam, India

    Kedar Nath Das

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Neha Yadav, Kim, J.H., Anupam Yadav (2016). Numerical Solution of a Class of Singular Boundary Value Problems Arising in Physiology Based on Neural Networks. In: Pant, M., Deep, K., Bansal, J., Nagar, A., Das, K. (eds) Proceedings of Fifth International Conference on Soft Computing for Problem Solving. Advances in Intelligent Systems and Computing, vol 437. Springer, Singapore. https://doi.org/10.1007/978-981-10-0451-3_60

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  • DOI: https://doi.org/10.1007/978-981-10-0451-3_60

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-0450-6

  • Online ISBN: 978-981-10-0451-3

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