Numerical solution of a class of singular boundary value problems arising in physiology based on neural networks

Neha Yadav; Joong Hoon Kim; Anupam Yadav

doi:10.1007/978-981-10-0451-3_60

Numerical solution of a class of singular boundary value problems arising in physiology based on neural networks

Neha Yadav, Joong Hoon Kim, Anupam Yadav

School of Civil, Environmental and Architectural Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Citation (Scopus)

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.

Original language	English
Title of host publication	Proceedings of 5th International Conference on Soft Computing for Problem Solving, SocProS 2015
Editors	Kusum Deep, Kedar Nath Das, Jagdish Chand Bansal, Millie Pant, Atulya Nagar
Publisher	Springer Verlag
Pages	673-681
Number of pages	9
ISBN (Print)	9789811004506
DOIs	https://doi.org/10.1007/978-981-10-0451-3_60
Publication status	Published - 2016
Event	5th International Conference on Soft Computing for Problem Solving, SocProS 2015 - Roorkee, India Duration: 2015 Dec 18 → 2015 Dec 20

Publication series

Name	Advances in Intelligent Systems and Computing
Volume	437
ISSN (Print)	2194-5357

Other

Other	5th International Conference on Soft Computing for Problem Solving, SocProS 2015
Country/Territory	India
City	Roorkee
Period	15/12/18 → 15/12/20

Keywords

Gradient descent algorithm
Neural networks
Singular boundary value problem

ASJC Scopus subject areas

Control and Systems Engineering
Computer Science(all)

Access to Document

10.1007/978-981-10-0451-3_60

Cite this

Yadav, N., Kim, J. H., & Yadav, A. (2016). Numerical solution of a class of singular boundary value problems arising in physiology based on neural networks. In K. Deep, K. N. Das, J. C. Bansal, M. Pant, & A. Nagar (Eds.), Proceedings of 5th International Conference on Soft Computing for Problem Solving, SocProS 2015 (pp. 673-681). (Advances in Intelligent Systems and Computing; Vol. 437). Springer Verlag. https://doi.org/10.1007/978-981-10-0451-3_60

Numerical solution of a class of singular boundary value problems arising in physiology based on neural networks. / Yadav, Neha; Kim, Joong Hoon; Yadav, Anupam.
Proceedings of 5th International Conference on Soft Computing for Problem Solving, SocProS 2015. ed. / Kusum Deep; Kedar Nath Das; Jagdish Chand Bansal; Millie Pant; Atulya Nagar. Springer Verlag, 2016. p. 673-681 (Advances in Intelligent Systems and Computing; Vol. 437).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Yadav, N, Kim, JH & Yadav, A 2016, Numerical solution of a class of singular boundary value problems arising in physiology based on neural networks. in K Deep, KN Das, JC Bansal, M Pant & A Nagar (eds), Proceedings of 5th International Conference on Soft Computing for Problem Solving, SocProS 2015. Advances in Intelligent Systems and Computing, vol. 437, Springer Verlag, pp. 673-681, 5th International Conference on Soft Computing for Problem Solving, SocProS 2015, Roorkee, India, 15/12/18. https://doi.org/10.1007/978-981-10-0451-3_60

Yadav N, Kim JH, Yadav A. Numerical solution of a class of singular boundary value problems arising in physiology based on neural networks. In Deep K, Das KN, Bansal JC, Pant M, Nagar A, editors, Proceedings of 5th International Conference on Soft Computing for Problem Solving, SocProS 2015. Springer Verlag. 2016. p. 673-681. (Advances in Intelligent Systems and Computing). doi: 10.1007/978-981-10-0451-3_60

Yadav, Neha ; Kim, Joong Hoon ; Yadav, Anupam. / Numerical solution of a class of singular boundary value problems arising in physiology based on neural networks. Proceedings of 5th International Conference on Soft Computing for Problem Solving, SocProS 2015. editor / Kusum Deep ; Kedar Nath Das ; Jagdish Chand Bansal ; Millie Pant ; Atulya Nagar. Springer Verlag, 2016. pp. 673-681 (Advances in Intelligent Systems and Computing).

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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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Numerical solution of a class of singular boundary value problems arising in physiology based on neural networks

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