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A stochastic numerical approach for a class of singular singularly perturbed system

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  • Zulqurnain Sabir
  • Thongchai Botmart
  • Muhammad Asif Zahoor Raja
  • Wajaree Weera
  • Fevzi Erdoğan

Abstract

In the present study, a neuro-evolutionary scheme is presented for solving a class of singular singularly perturbed boundary value problems (SSP-BVPs) by manipulating the strength of feed-forward artificial neural networks (ANNs), global search particle swarm optimization (PSO) and local search interior-point algorithm (IPA), i.e., ANNs-PSO-IPA. An error-based fitness function is designed using the differential form of the SSP-BVPs and its boundary conditions. The optimization of this fitness function is performed by using the computing capabilities of ANNs-PSO-IPA. Four cases of two SSP systems are tested to confirm the performance of the suggested ANNs-PSO-IPA. The correctness of the scheme is observed by using the comparison of the proposed and the exact solutions. The performance indices through different statistical operators are also provided to solve the SSP-BVPs using the proposed ANNs-PSO-IPA. Moreover, the reliability of the scheme is observed by taking hundred independent executions and different statistical performances have been provided for solving the SSP-BVPs to check the convergence, robustness and accuracy.

Suggested Citation

  • Zulqurnain Sabir & Thongchai Botmart & Muhammad Asif Zahoor Raja & Wajaree Weera & Fevzi Erdoğan, 2022. "A stochastic numerical approach for a class of singular singularly perturbed system," PLOS ONE, Public Library of Science, vol. 17(11), pages 1-19, November.
    • Handle: RePEc:plo:pone00:0277291
    DOI: 10.1371/journal.pone.0277291
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    1. Taghi Hosseinzadeh Khonakdari & Mehrdad Ahmadi Kamarposhti, 2021. "Real-time detection of microgrid islanding considering sources of uncertainty using type-2 fuzzy logic and PSO algorithm," PLOS ONE, Public Library of Science, vol. 16(9), pages 1-18, September.
    2. Feng Chen & Xun Gao & Xinghua Xia & Jing Xu, 2022. "Using LSTM and PSO techniques for predicting moisture content of poplar fibers by Impulse-cyclone Drying," PLOS ONE, Public Library of Science, vol. 17(4), pages 1-26, April.
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