Bio-inspired computational heuristics to study Lane-Emden systems arising in astrophysics model.
This study reports novel hybrid computational methods for the solutions of nonlinear singular Lane-Emden type differential equation arising in astrophysics models by exploiting the strength of unsupervised neural network models and stochastic optimization techniques. In the scheme the neural network, sub-part of large field called soft computing, is exploited for modelling of the equation in an unsupervised manner. The proposed approximated solutions of higher order ordinary differential equation are calculated with the weights of neural networks trained with genetic algorithm, and pattern search hybrid with sequential quadratic programming for rapid local convergence. The results of proposed solvers for solving the nonlinear singular systems are in good agreements with the standard solutions. Accuracy and convergence the design schemes are demonstrated by the results of statistical performance measures based on the sufficient large number of independent runs.
Department of Mathematics, University of Gujrat, Gujrat, 50700 Pakistan.
Iftikhar
I
Ahmad
Department of Electrical Engineering, COMSATS Institute of Information Technology, Attock, 43600 Pakistan.
Muhammad Asif Zahoor
MA
Raja
Faculty of Science and Technology, University of Malaysia Pahang, Pekan, Pahang Malaysia.
Muhammad
M
Bilal
Department of Mathematics, University of Gujrat, Gujrat, 50700 Pakistan.
Farooq
F
Ashraf
Artificial neural networks; Computational intelligence; Genetic algorithm; Pattern search methods; Sequential quadratic programming; Singular systems