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


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Sabir Z., Botmart T., Raja M. A. Z., Weera W., Erdoğan F.

PLoS ONE, vol.17, no.11 November, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 17 Issue: 11 November
  • Publication Date: 2022
  • Doi Number: 10.1371/journal.pone.0277291
  • Journal Name: PLoS ONE
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Agricultural & Environmental Science Database, Animal Behavior Abstracts, Aquatic Science & Fisheries Abstracts (ASFA), BIOSIS, Biotechnology Research Abstracts, Chemical Abstracts Core, EMBASE, Food Science & Technology Abstracts, Index Islamicus, Linguistic Bibliography, MEDLINE, Pollution Abstracts, Psycinfo, zbMATH, Directory of Open Access Journals
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

Copyright: © 2022 Sabir et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.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.