Nature-inspired computing approach for solving non-linear singular Emden–Fowler problem arising in electromagnetic theory

Junaid Ali Khan, Muhammad Asif Zahoor Raja, Mohammad Mehdi Rashidi, Muhammad Ibrahim Syam, Abdul Majid Wazwaz

Research output: Contribution to journalArticlepeer-review

95 Citations (Scopus)

Abstract

In this research, the well-known non-linear Lane–Emden–Fowler (LEF) equations are approximated by developing a nature-inspired stochastic computational intelligence algorithm. A trial solution of the model is formulated as an artificial feed-forward neural network model containing unknown adjustable parameters. From the LEF equation and its initial conditions, an energy function is constructed that is used in the algorithm for the optimisation of the networks in an unsupervised way. The proposed scheme is tested successfully by applying it on various test cases of initial value problems of LEF equations. The reliability and effectiveness of the scheme are validated through comprehensive statistical analysis. The obtained numerical results are in a good agreement with their corresponding exact solutions, which confirms the enhancement made by the proposed approach.

Original languageEnglish
Pages (from-to)377-396
Number of pages20
JournalConnection Science
Volume27
Issue number4
DOIs
Publication statusPublished - Oct 2 2015

Keywords

  • computational intelligence
  • hybrid computing
  • interior-point method
  • neural networks
  • particle swarm optimisation
  • pattern search
  • singular initial value problems

ASJC Scopus subject areas

  • Software
  • Human-Computer Interaction
  • Artificial Intelligence

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