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Neural Network Solution of Single-Delay Differential Equations

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Abstract

Following the ideas of Lagaris et al. (IEEE Trans Neural Netw 9(5):987–1000, 1998), we use Neural Networks to solve approximatively first-order single-delay differential equations and systems. We apply the proposed novel methodology to various problems with constant delay terms and the resulted continuous solutions prove to be very efficient. This is the case not only for nonstiff problems but for equations with stiffness too.

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Authors and Affiliations

  1. School of Electronics and Information Engineering, Fuqing Branch of Fujian Normal University, Fuqing, 350300, China

    Jie Fang

  2. Department of Computer Science and Technology, Neusoft Institute Guangdong, Foshan, 528228, China

    Chenglian Liu

  3. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, China

    T. E. Simos

  4. South Ural State University, 76, Lenin Aven., Chelyabinsk, Russia, 454080

    T. E. Simos

  5. Group of Modern Computational Methods, Ural Federal University, 19 Mira st., 620002, Yekaterinburg, Russian Federation

    T. E. Simos

  6. Data Recovery Key Laboratory of Sichuan Province, Neijiang Normal University, Dongtong Road 705, Neijiang, 641100, China

    T. E. Simos

  7. Section of Mathematics, Department of Civil Engineering, Democritus University of Thrace, Xanthi, Greece

    T. E. Simos

  8. microSENSES Laboratory, Department of Electrical and Electronic Engineering, University of West Attica, Athens, Greece

    I. Th. Famelis

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  1. Jie Fang
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  2. Chenglian Liu
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  4. I. Th. Famelis
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Correspondence to T. E. Simos.

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Fang, J., Liu, C., Simos, T.E. et al. Neural Network Solution of Single-Delay Differential Equations. Mediterr. J. Math. 17, 30 (2020). https://doi.org/10.1007/s00009-019-1452-5

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  • DOI: https://doi.org/10.1007/s00009-019-1452-5

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