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Morlet Wavelet Neural Network Investigations to Present the Numerical Investigations of the Prediction Differential Model

Author

Listed:
  • Zulqurnain Sabir

    (Department of Computer Science and Mathematics, Lebanese American University, Beirut 1401, Lebanon)

  • Adnène Arbi

    (Laboratory of Engineering Mathematics (LR01ES13), Tunisia Polytechnic School, University of Carthage, Tunis 2078, Tunisia
    Department of Advanced Sciences and Technologies at National School of Advanced Sciences and Technologies of Borj Cedria, University of Carthage, Hammam-Chott 1164, Tunisia)

  • Atef F. Hashem

    (Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 13318, Saudi Arabia
    Department of Mathematics and Information Science, Faculty of Science, Beni-Suef University, Beni-Suef 62514, Egypt)

  • Mohamed A Abdelkawy

    (Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 13318, Saudi Arabia
    Department of Mathematics and Information Science, Faculty of Science, Beni-Suef University, Beni-Suef 62514, Egypt)

Abstract

In this study, a design of Morlet wavelet neural networks (MWNNs) is presented to solve the prediction differential model (PDM) by applying the global approximation capability of a genetic algorithm (GA) and local quick interior-point algorithm scheme (IPAS), i.e., MWNN-GAIPAS. The famous and historical PDM is known as a variant of the functional differential system that works as theopposite of the delay differential models. A fitness function is constructed by using the mean square error and optimized through the GA-IPAS for solving the PDM. Three PDM examples have been presented numerically to check the authenticity of the MWNN-GAIPAS. For the perfection of the designed MWNN-GAIPAS, the comparability of the obtained outputs and exact results is performed. Moreover, the neuron analysis is performed by taking 3, 10, and 20 neurons. The statistical observations have been performed to authenticate the reliability of the MWNN-GAIPAS for solving the PDM.

Suggested Citation

  • Zulqurnain Sabir & Adnène Arbi & Atef F. Hashem & Mohamed A Abdelkawy, 2023. "Morlet Wavelet Neural Network Investigations to Present the Numerical Investigations of the Prediction Differential Model," Mathematics, MDPI, vol. 11(21), pages 1-20, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:21:p:4480-:d:1270054
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    References listed on IDEAS

    as
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    2. Zou, Dexuan & Li, Steven & Kong, Xiangyong & Ouyang, Haibin & Li, Zongyan, 2019. "Solving the combined heat and power economic dispatch problems by an improved genetic algorithm and a new constraint handling strategy," Applied Energy, Elsevier, vol. 237(C), pages 646-670.
    3. Zulqurnain Sabir & Juan L. G. Guirao & Tareq Saeed & Fevzi Erdoğan, 2020. "Design of a Novel Second-Order Prediction Differential Model Solved by Using Adams and Explicit Runge–Kutta Numerical Methods," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-7, July.
    4. Mayer, Martin János & Szilágyi, Artúr & Gróf, Gyula, 2020. "Environmental and economic multi-objective optimization of a household level hybrid renewable energy system by genetic algorithm," Applied Energy, Elsevier, vol. 269(C).
    5. Sabir, Zulqurnain & Wahab, Hafiz Abdul & Umar, Muhammad & Erdoğan, Fevzi, 2019. "Stochastic numerical approach for solving second order nonlinear singular functional differential equation," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
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