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Neuro-Swarm heuristic using interior-point algorithm to solve a third kind of multi-singular nonlinear system.

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

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|September 14, 2021
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Summary

This study introduces a novel neuro-swarm computing solver, artificial neural networks (ANNs) optimized with particle swarm optimization (PSO) and interior-point algorithm (IPA), to solve complex nonlinear Emden-Fowler equations.

Keywords:
artificial neural networkshybrid approachinterior-point algorithmmulti-singularnonlinear singular systemstatistical analysis

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Area of Science:

  • Computational Mathematics
  • Numerical Analysis
  • Applied Physics

Background:

  • Nonlinear systems, particularly the Emden-Fowler equations, present significant challenges in numerical solutions.
  • Existing methods may struggle with multi-singular and third-order nonlinearities inherent in these systems.

Purpose of the Study:

  • To develop and validate a robust computational framework for solving a specific class of multi-singular, third-order nonlinear Emden-Fowler equations.
  • To introduce the artificial neural networks (ANNs) optimized with particle swarm optimization (PSO) and interior-point algorithm (IPA) (ANN-PSO-IPA) as a novel solver.

Main Methods:

  • Designing an objective function utilizing the continuous mapping capabilities of ANNs.
  • Employing a hybrid optimization approach combining PSO and IPA (PSO-IPA) for fitness function optimization.
  • Testing the ANN-PSO-IPA solver on three distinct nonlinear variants of the Emden-Fowler system.

Main Results:

  • The ANN-PSO-IPA demonstrated high precision and reliability in solving the targeted nonlinear systems.
  • Consistent and accurate numerical results were obtained across multiple executions.
  • The framework proved effective for handling the complexities of multi-singular, third-order nonlinearities.

Conclusions:

  • The proposed ANN-PSO-IPA solver offers a feasible and reliable method for addressing challenging nonlinear Emden-Fowler equations.
  • This neuro-swarm computing approach provides a viable alternative to traditional numerical techniques for complex systems.
  • The study validates the efficacy and precision of the integrated ANN-PSO-IPA framework.