[1] A. M. Wazwaz, A new algorithm for solving diferential equations of Lane-Emden type, Appl. Math. Comput, 118, 2001, 287–310Google Scholar

[2] M. Dehghan, F. Shakeri, Approximate solution of a differential equation arising in astrophysics using the variational iteration method, New Astron, 13(1), 2008, 53–59Web of ScienceCrossrefGoogle Scholar

[3] K. Parand, M. Shahini, M. Dehghan, Rational Legendre pseudospectral approach for solving nonlinear differential equations of Lane-Emden type, J. Comput. Phys, 228(23), 2009, 8830–8840Web of ScienceGoogle Scholar

[4] K. Parand, A. Pirkhedri, Sinc-Collocation method for solving astrophysics equations, New Astron, 15(6), 2010, 533–537Web of ScienceCrossrefGoogle Scholar

[5] K. Boubaker, R. A. Van Gorder, Application of the BPES to Lane-Emden equations governing polytropic and isothermal gas spheres, New Astron, 17(6), 2012, 565–569CrossrefWeb of ScienceGoogle Scholar

[6] R.K. Pandey, N. Kumar, A. Bhardwaj, G. Dutta, Solution of Lane-Emden type equations using Legendre operational matrix of differentiation, Appl. Math. Comput, 218(14), 2012, 7629–7637Web of ScienceGoogle Scholar

[7] A.M. Rismani, H. Monfared, Numerical solution of singular IVPs of Lane-Emden type using a modified Legendre-spectral method, Appl. Math. Model, 36(10), 2012, 4830–4836CrossrefWeb of ScienceGoogle Scholar

[8] E.H. Doha, W.M. Abd-Elhameed, Y.H. Youssri, Second kind Chebyshev operational matrix algorithm for solving differential equations of Lane-Emden type, New Astron, 23-24, 2013, 113–117Web of ScienceCrossrefGoogle Scholar

[9] H. Kaur, R.C. Mittal, V. Mishra, Haar wavelet approximate solutions for the generalized Lane-Emden equations arising in astrophysics, Comput. Phys. Commun, 184(9), 2013, 2169–2177Web of ScienceGoogle Scholar

[10] A. Nazari-Golshan, S.S. Nourazar, H. Ghafoori-Fard, A. Yildirim, A. Campo, A modified homotopy perturbation method coupled with the Fourier transform for nonlinear and singular Lane-Emden equations, Appl. Math. Lett, 26, 2013, 1018–1025Web of ScienceCrossrefGoogle Scholar

[11] B. Grbz, M. Sezer, Laguerre polynomial approach for solving Lane-Emden type functional differential equations, Appl. Math. Comput, 242, 2014, 255–264Web of ScienceGoogle Scholar

[12] S. Mall, S. Chakraverty, Chebyshev Neural Network based model for solving Lane–Emden type equations, Appl. Math. Comput, 247, 2014, 100–114Web of ScienceGoogle Scholar

[13] P. Pablo, C. Alzate, An Iterative Method for Solving Two Special Cases of Lane-Emden Type Equation, AJCM, 4, 2014, 242–253CrossrefGoogle Scholar

[14] Z. Łmarda, Y. Khan, An efficient computational approach to solving singular initial value problems for Lane–Emden type equations, J. Comput. Appl. Math, 290, 2015, 65–73Web of ScienceGoogle Scholar

[15] A. Kazemi Nasab, A. Kılıman, Z. P. Atabakan, W.J. Leong, A numerical approach for solving singular nonlinear Lane–Emden type equations arising in astrophysics, New Astron, 34, 2015, 178–186Web of ScienceCrossrefGoogle Scholar

[16] R. Iacono, M. De Felice, Constructing analytic approximate solutions to the Lane–Emden equation, Phys. Lett. A, 379(32-33), 2015, 1802–1807Web of ScienceGoogle Scholar

[17] L.P. Aarts, P. V. Veer, Neural Network Method for Solving Partial Differential Equations, Neural process lett., 14, 2001, 261–271CrossrefGoogle Scholar

[18] A. J. Meade, The Numerical Solution of Linear Ordinary Differential Equations by Feedforward Neural Networks, Mathl. Comput Modelling, 19(12), 1994, 1-25Google Scholar

[19] D. R. Parisi, C. Mariani, and M. A. Laborde, Solving differential equations with unsupervised neural networks, Chem. Eng. Process. Process Intensif., 42, 2003, 715–721CrossrefGoogle Scholar

[20] I. E. Lagaris, A. C. Likas, and D. I. Fotiadis, Artifical Neural Networks for Solving Ordinary and Partial Differential Equations, Neural Networks, IEEE Trans., 9(5), 1998, 1–26Google Scholar

[21] L. Jianyu, L. Siwei, Q. Yingjian, H. Yaping, Numerical solution of elliptic partial differential equation using radial basis function neural networks, Neural Networks, 16, 2003, 729–734CrossrefGoogle Scholar

[22] A. Malek, R. S. Beidokhti, Numerical solution for high order differential equations using a hybrid neural network – Optimization method, Appl. Math. Comput., 183, 2006, 260–271Google Scholar

[23] F. Fazayeli, L. P. Wang, and W. Liu, Back-propagation with chaos, Proc. 2008IEEE International Conference on Neural Networks and Signal Processing(ICNNSP2008), Zhenjiang, China, June 7-11, pp.5-8, 2008Google Scholar

[24] K. Parand, Z. Roozbahani, Solving nonlinear Lane-Emden type equations with unsupervised combined artificial neural networks, Int. J. of Industrial Math., 5, 2013, 355–366Google Scholar

[25] V. Kecman, Learning and Soft Computing, Support Vector machines, NeuralNetworks and Fuzzy Logic Models, The MIT Press, Cambridge, MA, 2001Google Scholar

[26] L.P. Wang and X.J. Fu, Data Mining with Computational Intelligence, Springer, Berlin, 2005Google Scholar

[27] J.C. Patra, P.K. Meher, G. Chakraborty, Nonlinear channel equalization for wireless communication systems using Legendre neural networks, Signal Processing, 89(11), 2009, 2251–2262Web of ScienceGoogle Scholar

[28] S.K. Nanda, D.P. Tripathy, Application of Functional Link Artificial Neural Network for Prediction of Machinery Noise in Opencast Mines, Adv. Fuzzy Syst, 2011, 2011, 1–11CrossrefGoogle Scholar

[29] K.K. Das, J.K. Satapathy, Novel Algorithms Based on Legendre Neural Network for Nonlinear Active Noise Control with Nonlinear Secondary Path, IJCSIT, 3(5), 2012, 5036–5039Google Scholar

[30] Y. H. Pao, Y. Takefuji, Functional-Link Net Computing: Theory, System, Architecture and Functionalities, Computer, 25(5), 1992, 76–79CrossrefGoogle Scholar

[31] K. A. Dowsland, Hill-Climbing, Simulated Annealing and the Steiner Problem in Graphs, Eng. Optim, 17, 1991, 91–107CrossrefGoogle Scholar

[32] B. Caruntu, C. Bota, Approximate polynomial solutions of the nonlinear Lane-Emden type equations arising in astrophysics using the squared remainder minimization method, Comput. Phys. Commun, 184, 2013, 1643–1648Web of ScienceCrossrefGoogle Scholar

[33] J. A. Khan, M. A. Z. Raja, I. M. Qureshi, Numerical treatment of nonlinear Emden–Fowler equation using stochastic technique, Ann Math Artif Intell, 63(2), 2011, 185–207CrossrefWeb of ScienceGoogle Scholar

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