References
- G. Adomian, R. Rach, and N.T. Shawagfeh, On the analytic solution of the Lane-Emden equation, Found. Phys. Lett. 8 (1995), pp. 161–181.
- A. Aslanov, Approximate solutions of Emden-Fowler type equations, Int. J. Comput. Math 86 (2009), pp. 807–826.
- A. Aslanov, On the existence of a solution of a second-order singular initial value problem, Math. Methods Appl. Sci. 38 (2015), pp. 980–990.
- A.H. Bhrawy and A.S. Alofi, A Jacobi-Gauss collocation method for solving nonlinear Lane-Emden type equations, Commun. Nonlinear Sci. Numer. Simul. 17 (2012), pp. 62–70.
- L. Bin, A new numerical scheme for third-order singularly Emden-Fowler equations using quintic B-spline function, Int. J. Comput. Math 98 (2021), pp. 2406–2422.
- M. Bisheh Niasar, A computational method for solving the Lane-Emden initial value problems, Comput. Methods Differ. Equ. 8 (2020), pp. 673–684.
- J.P. Boyd, Chebyshev spectral methods and the Lane-Emden problem, Numer. Math. Theory Methods Appl. 4 (2011), pp. 142–157.
- C. Brezinski and J. Van Iseghem, A taste of Padé approximation, Acta Numer. 4 (1995), pp. 53–103.
- H. Brunner, Collocation Methods for Volterra Integral and Related Functional Equations, Cambridge University Press, Cambridge, 2004.
- M.S.H. Chowdhury and I. Hashim, Solutions of Emden-Fowler equations by homotopy-perturbation method, Nonlinear Anal. Real World Appl. 10 (2009), pp. 104–115.
- P.J. Davis and P. Rabinowitz, Methods of Numerical Integration, 2nd ed., Academic Press, New York, 1984.
- M. Dehghan and F. Shakeri, Approximate solution of a differential equation arising in astrophysics using the variational iteration method, New Astron. 13 (2008), pp. 53–59.
- R.H. Fowler, Further studies of Emden's and similar differential equations, Q. J. Math. 2 (1931), pp. 259–288.
- B.Y. Guo and J.P. Yan, Legendre-Gauss collocation method for initial value problems of second order ordinary differential equations, Appl. Numer. Math. 59 (2009), pp. 1386–1408.
- J.A. Khan, M.A.Z. Raja, M.M. Rashidi, M.I. Syam, and A.M. Wazwaz, Nature-inspired computing approach for solving non-linear singular Emden-Fowler problem arising in electromagnetic theory, Connection Sci. 27 (2015), pp. 377–396.
- D. Krtinić and M. Mikić, Existence and uniqueness of solutions of some Cauchy problems for the Emden-Fowler equation, Differ. Equ. 57 (2021), pp. 984–992.
- G.T. Marewo, A modified spectral relaxation method for some Emden-Fowler equations, in Recent Advances in Numerical Simulations, chap. 7, IntechOpen, Rijeka, 2021, pp. 1–14.
- J.C. Mason and D. Handscomb, Chebyshev Polynomials, Chapman & Hall/CRC, Boca Raton, FL, 2003.
- M.A. Mehrpouya, An efficient pseudospectral method for numerical solution of nonlinear singular initial and boundary value problems arising in astrophysics, Math. Methods Appl. Sci. 39 (2016), pp. 3204–3214.
- Z. Nehari, On a nonlinear differential equation arising in nuclear physics, Proc. R. Ir. Acad. Sect. A62 (1963), pp. 117–135.
- K. Parand, M. Shahini, and M. Dehghan, Rational Legendre pseudospectral approach for solving nonlinear differential equations of Lane-Emden type, J. Comput. Phys. 228 (2009), pp. 8830–8840.
- R.V. Ramnath, On a class of nonlinear differential equations of astrophysics, J. Math. Anal. Appl. 35 (1971), pp. 27–47.
- A.M. Rismani and H. Monfared, Numerical solution of singular IVPs of Lane-Emden type using a modified Legendre-spectral method, Appl. Math. Model. 36 (2012), pp. 4830–4836.
- P. Roul, H. Madduri, and R. Agarwal, A fast-converging recursive approach for Lane-Emden type initial value problems arising in astrophysics, J. Comput. Appl. Math. 359 (2019), pp. 182–195.
- N.T. Shawagfeh, Nonperturbative approximate solution for Lane-Emden equation, J. Math. Phys. 34 (1993), pp. 4364–4369.
- J. Shen, T. Tang, and L.L. Wang, Spectral Methods: Algorithms, Analysis and Applications, Springer, New York, 2011.
- H. Singh, An efficient computational method for the approximate solution of nonlinear Lane-Emden type equations arising in astrophysics, Astrophys. Space Sci. 363 (2018), Article ID 71.
- Z. Šmarda and Y. Khan, An efficient computational approach to solving singular initial value problems for Lane-Emden type equations, J. Comput. Appl. Math. 290 (2015), pp. 65–73.
- M. Taghipour and H. Aminikhah, Application of Pell collocation method for solving the general form of time-fractional Burgers equations, Math. Sci. (2022). Online.
- T. Tang, X. Xu, and J. Cheng, On spectral methods for Volterra integral equations and the convergence analysis, J. Comput. Math. 26 (2008), pp. 825–837.
- S. Tomar, An effective approach for solving a class of nonlinear singular boundary value problems arising in different physical phenomena, Int. J. Comput. Math 98 (2021), pp. 2060–2077.
- T.K. Wang, Z.F. Liu, and Y.T. Kong, The series expansion and Chebyshev collocation method for nonlinear singular two-point boundary value problems, J. Eng. Math. 126 (2021), Article ID 5.
- A.M. Wazwaz and S.A. Khuri, The variational iteration method for solving the Volterra integro-differential forms of the Lane-Emden and the Emden-Fowler problems with initial and boundary value conditions, Open Eng. 5 (2015), pp. 31–41.
- A.M. Wazwaz, R. Rach, and J.S. Duan, Adomian decomposition method for solving the Volterra integral form of the Lane-Emden equations with initial values and boundary conditions, Appl. Math. Comput. 219 (2013), pp. 5004–5019.
- J.S.W. Wong, On the generalized Emden-Fowler equation, SIAM Rev. 17 (1975), pp. 339–360.
- S.H. Xiang, On interpolation approximation: Convergence rates for polynomial interpolation for functions of limited regularity, SIAM J. Numer. Anal. 54 (2016), pp. 2081–2113.