Numerical solution of Lane-Emden type equations using Flatlet oblique multiwavelets collocation approach

[1] H. Adibi and A.M. Rismani, On using a modified Legendre-spectral method for solving singular IVPs of Lane-Emden type, Comput. Math. Appl. 60 (2010), 2126–2130.

[2] B. Alpert, textitA class of basis in L2 for the sparse representation of integral operators, SIAM J. Math. Anal. 24 (1993), no. 1, 246–262.

[3] B. Alpert, G. Beylkin, R.R. Coifman and V. Rokhlin, Wavelet-like basis for the fast solution of second-kind integral equations, SIAM J. Sci. Statist. Comput. 14 (1993), no. 1, 159–184.

[4] C.M. Bender, K.A. Milton, S.S. Pinsky and Simmons, A new perturbative approach to nonlinear problems, J. Math. Phys. 30 (1989), 1447-–1455.

[5] A.H. Bhrawy and A.S. Alofi, A JacobiGauss collocation method for solving nonlinear LaneEmden type equations, Commun. Nonlinear. Sci. 17 (2012), 62–70.

[6] J.P. Boyd, Chebyshev spectral methods and the Lane-Emden problem, Numer. Math. Theor. Meth. Appl. 4 (2011), 142–157.

[7] Li-hong Cui, Zheng-xing Cheng, A method of construction for biorthogonal multiwavelets system with 2 multiplicity, Appl. Math. Comput. 167 (2005), 901–918.

[8] W. Dahmen, B. Han, R.Q. Jia and A. Kunoth, Biorthogonal multiwavelets on the interval: cubic Hermite spline, Constr. Approximation 16 (2000), no. 2, 221–259.

[9] M.R.A. Darani, H. Adibi and M. Lakestani, Numerical solution of integrodifferential equations using flatlet oblique multiwavelets, Dyn. Contin. Discrete Impuls. Syst. Ser. A: Math. Anal. 17 (2010), 55–57.

[10] I. Daubechies, Orthonormal bases of compactly supported wavelets, Comm. Pure Appl. Math. 41 (1988) 909-996.

[11] I. Daubechies, Ten Lectures on Wavelets,  CBMS-NSF Lecture Notes, vol. 61, SIAM. 1992.

[12] M. Dehgan, m. Shakourifar and A. Hamidi, The solution of linear and nonlinear systems of Volterra functional equations using AdomianPade techniques, Chaos Soliton Fractals 39 (2009), 2509–2521.

[13] T.N.T. Goodman and S.L. Lee, Wavelets of multiplicity, Trans. Amer. Math. Soc. 342 (1994) 307-324.

[14] J.C. Goswami, A.K. Chan and C.K. Chui, On solving first-kind integral equations using wavelets on bounded interval, IEEE Trans. Antennas Propag. 43 (1995) 614-622.

[15] B. Han and Q.T. Jiang, Multiwavelets on the interval, Appl. Comput. Harmon. Anal. 12 (2002), 100–127.

[16] C. H. Hsiao, W. J. Wang, Optimal control of linear time-varying systems via Haar wavelets, J. Optim. Theory Appl. 103 (1999), no. 3, 641–655.

[17] S. Islam, I. Aziz and M Fayyaz, A new approach for numerical solution of integro-differential equations via Haar wavelets, Int. J. Comp. Math. 90 (2013), no. 9, 1971–1989.

[18] F. Keinert, Wavelets and Multiwavelets, Chapman and Hall/CRC, A CRC Press Company, Boca Raton London New York Washington D.C., 2003.

[19] M. Lakestani and M. Dehgan, Four techniques based on the B-spline expansion and the collocation approach for the numerical solution of the Lane–Emden equation, Math. Meth. Appl. Sci. 36 (2013), no. 16, 2243–2253.

[20] M. Lakestani and Z. Shafinejhad, Numerical solution Of linear integral equation using Flatlet oblique multiwavelets, Math. Aterna. 2 (2012), no. 2, 123–143.

[21] H.R. Marzban, H.R. Tabrizidooz and M. Razzaghi, Hybrid functions for nonlinear initial-value problems with applications to Lane–Emden type equations, Phys. Lett. A 372 (2008), 5883—5886.

[22] R. Mohammadzadeh, M. Lakestani and M. Dehgan, Collocation method for the numerical solutions of Lane–Emden type equations using cubic Hermite spline functions, Math. Meth. Appl. Sci. 37 (2014), no. 9, 1303–1717.

[23] K. Parand, M. Dehghan, A.R. Rezaei and S.M. Ghaderi, An approximate algorithm for the solution of the nonlinear LaneEmden type equations arising in astrophysics using Hermite function collocation method, Comput. Phys. Commun. 181 (2010), 1096–1108.

[24] O.W. Richarson, The emission of electricity from hot bodies, Longmans, Green and Company, 1921.

[25] A.M. Wazwaz, A new algorithm for solving differential equations of Lane-Emden type, Appl. Math. Comput. 118 (2001), 287–310.

[26] A.M. Wazwaz, The modified decomposition method for analytic treatment of differential equations, Appl. Math. Comput. 173 (2006), 165–176.

[27] X.G. Xia, J.S. Geronimo, D.P. Hardin and B.E. Suter, Design of Prefilters for Discete Multiwavelet Transform, IEEE Trans. Signal Process. 44 (1996), 25–35.

[28] S. Yzbasi and M. Sezer, An improved Bessel collocation method with a residual error function to solve a class of LaneEmden differential equations, Math. Comput. Model. 57 (2013), 1298–1311.

[29] S. Yzbasi and M. Sezer, An improved Bessel collocation method with a residual error function to solve a class of LaneEmden differential equations, Math. Comput. Model. 57 (2013), 1298–1311.

[30] A. Zamiri, A. Borhanifar and A. Ghannadiasl, Laguerre collocation method for solving Lane-Emden type equations, 9 (2021), no. 4, 1176–1197

[31] H. Zhu, J. Niu, R. Zhang and Y. Lin, A new approach for solving nonlinear singular boundary value problems, Math. Model. Anal. 23 (2018), 33–43.