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Integrated intelligent computing paradigm for nonlinear multi-singular third-order Emden–Fowler equation

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Abstract

In this study, an advance computational intelligence scheme is designed and implemented to solve third-order nonlinear multiple singular systems represented with Emden–Fowler differential equation (EFDE) by exploiting the efficacy of artificial neural networks (ANNs), genetic algorithms (GAs) and active-set algorithm (ASA), i.e., ANN–GA–ASA. In the scheme, ANNs are used to discretize the EFDE for formulation of mean squared error-based fitness function. The optimization task for ANN models of nonlinear multi-singular system is performed by integrated competency GA and ASA. The efficiency of the designed ANN–GA–ASA is examined by solving five different variants of the singular model to check the effectiveness, reliability and significance. The statistical investigations are also performed to authenticate the precision, accuracy and convergence.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan

    Zulqurnain Sabir & Muhammad Umar

  2. Department of Applied Mathematics and Statistics, Technical University of Cartagena, Hospital de Marina, 30203, Cartagena, Spain

    Juan L. G. Guirao

  3. Department of Mathematics, COMSATS University Islamabad, Attock Campus, Attock, 43600, Pakistan

    Muhammad Shoaib

  4. Department of Electrical and Computer Engineering, COMSATS University Islamabad, Attock Campus, Attock, 43600, Pakistan

    Muhammad Asif Zahoor Raja

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  1. Zulqurnain Sabir
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  2. Muhammad Umar
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  3. Juan L. G. Guirao
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  4. Muhammad Shoaib
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  5. Muhammad Asif Zahoor Raja
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Correspondence to Juan L. G. Guirao.

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Sabir, Z., Umar, M., Guirao, J.L.G. et al. Integrated intelligent computing paradigm for nonlinear multi-singular third-order Emden–Fowler equation. Neural Comput & Applic 33, 3417–3436 (2021). https://doi.org/10.1007/s00521-020-05187-w

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  • DOI: https://doi.org/10.1007/s00521-020-05187-w

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