TY - JOUR
T1 - Nature-inspired computing approach for solving non-linear singular Emden–Fowler problem arising in electromagnetic theory
AU - Khan, Junaid Ali
AU - Raja, Muhammad Asif Zahoor
AU - Rashidi, Mohammad Mehdi
AU - Syam, Muhammad Ibrahim
AU - Wazwaz, Abdul Majid
N1 - Publisher Copyright:
© 2015 Taylor & Francis.
PY - 2015/10/2
Y1 - 2015/10/2
N2 - 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.
AB - 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.
KW - computational intelligence
KW - hybrid computing
KW - interior-point method
KW - neural networks
KW - particle swarm optimisation
KW - pattern search
KW - singular initial value problems
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U2 - 10.1080/09540091.2015.1092499
DO - 10.1080/09540091.2015.1092499
M3 - Article
AN - SCOPUS:84957852177
SN - 0954-0091
VL - 27
SP - 377
EP - 396
JO - Connection Science
JF - Connection Science
IS - 4
ER -