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Design of stochastic numerical solver for the solution of singular three-point second-order boundary value problems

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Abstract

In this paper, a novel meta-heuristic computing solver is presented for solving the singular three-point second-order boundary value problems using artificial neural networks (ANNs) optimized by the combined strength of global and local search ability of genetic algorithms (GAs) and interior point algorithm (IPA), i.e., ANN–GA–IPA. The inspiration for presenting this numerical work comes from the intention of introducing a consistent framework that combines the effective features of neural networks optimized with the contexts of soft computing to handle with such challenging systems. Three numerical variants of singular second-order system have been taken to examine the proficiency, robustness, and stability of the designed approach. The comparison of the proposed results of ANN–GA–IPA from available exact solutions shows the good agreement with 5 to 7 decimal places of the accuracy which established worth of the methodology through performance analyses on a single and multiple executions.

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Authors and Affiliations

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

    Zulqurnain Sabir

  2. Department of Mathematics, Cankaya University, Ankara, Turkey

    Dumitru Baleanu

  3. Insitute of Space Science, Magurele-Bucharest, Romania

    Dumitru Baleanu

  4. Department of Mathematics, COMSATS University Islamabad, Attock Campus, Attock, Pakistan

    Muhammad Shoaib

  5. Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, 64002, Yunlin, Taiwan, ROC

    Muhammad Asif Zahoor Raja

  6. Department Electrical and Computer Engineering, COMSATS University Islamabad, Attock Campus, Attock, Pakistan

    Muhammad Asif Zahoor Raja

Authors
  1. Zulqurnain Sabir
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  2. Dumitru Baleanu
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  3. Muhammad Shoaib
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  4. Muhammad Asif Zahoor Raja
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Correspondence to Dumitru Baleanu.

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Sabir, Z., Baleanu, D., Shoaib, M. et al. Design of stochastic numerical solver for the solution of singular three-point second-order boundary value problems. Neural Comput & Applic 33, 2427–2443 (2021). https://doi.org/10.1007/s00521-020-05143-8

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  • DOI: https://doi.org/10.1007/s00521-020-05143-8

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