# Journal of Advances in Applied Mathematics

### Discontinuous Legendre Wavelet Galerkin Method for Solving Lane-Emden Type Equation

Download PDF (611.5 KB) PP. 29 - 43 Pub. Date: January 1, 2016

### Author(s)

**Xiaoyang Zheng**^{*}

College of Mathematics and Statistics, Chongqing University of Technology, 400054, Chongqing, China**Zhengyuan Wei**

College of Mathematics and Statistics, Chongqing University of Technology, 400054, Chongqing, China**Jiangping He**

College of Mathematics and Statistics, Chongqing University of Technology, 400054, Chongqing, China

### Abstract

### Keywords

### References

[1] Davis, H.T. Introduction to Nonlinear Differential and Integral Equations. Dover, New York (1962)

[2] Chandrasekhar, S. Introduction to Study of Stellar Structure. Dover, New York (1967)

[3] N.T. Shawagfeh, N.T. “Nonperturbative approximate solution for Lane–Emden equation.” J. Math. Phys. 34 (9), 4364-4369 (1993)

[4] Singh, O.P., Pandey, R.K., Singh, V.K. “An analytic algorithm for Lane–Emden equations arising in Astrophysics using MHAM. Comput.” Phys. Commun. 180, 1116-1124 (2009)

[5] Wazwaz, A.M. “A new algorithm for solving differential equation Lane–Emden type.” Appl. Math. Comput. 118, 287-310 (2001)

[6] Liao, S.J. “A new analytic algorithm of Lane–Emden type equations.” Appl. Math. Comput. 142, 1-16 (2003)

[7] Iqbal, S. and A. Javed, “Application of optimal homotopy asymptotic method for the analytic solution of singular Lane–Emden type equation.” Appl. Math. Comput. 217, 7753--7761 (2011)

[8] He, J.H. “Variational approach to the Lane–Emden equation.” Appl. Math. Comput. 143, 539-541 (2003)

[9] Dehghan, M.F., Shakeri, F. “Approximate solution of a differential equation arising in astrophysics using variational iteration method.” New Astron. 13, 53-59 (2008)

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

[11] Van Gorder, R.A. “An elegant perturbation solution for the Lane–Emden equation of the second kind.” New Astron. 16 , 65-67 (2011).

[12] Van Gorder, R.A. “Analytical solutions to a quasilinear differential equation related to the Lane–Emden equation of the second kind. Celestial Mech.” Dynam. Astron. 109, 137-145 (2011)

[13] Razzaghi, M., Yousefi, S. “The Legendre wavelets Operational Matrix of Integration,” International Journal of Systems Science. 32, 500-502 (2001)

[14] Yousefi, S. “Legendre wavelets method for solving differential equations of Lane-Emden type,” Appl. Math. Comput. 181, 1417-1422 (2006)

[15] Razzaghi, M., Yousefi, S. “Legendre wavelets method for the solution of nonlinear problems in the calculus of variations.” Math. Comput. Model. 34, 45-54 (2001)

[16] Mohammadi, F., Hosseini, M.M. “A new Legendre wavelet operational matrix of derivative and its applications in solving the singular ordinary differential equations.” Journal of the Franklin Institute. 348, 1787-1796 (2011)

[17] Pandey, Rajesh K., Kumar, Narayan. “Abhinav Bhardwaj and Goutam Dutta, Solution of Lane–Emden type equations using Legendre operational matrix of differentiation.” Applied Mathematics and Computation. 218, 7629-7637 (2012)

[18] Mohammadi, F.M., Hosseini, M.M, Mohyud-din, S.T. “Legendre wavelet Galerkin method for solving ordinary differential equations with nonanalytic solution.” Int. J. Syst. Sci. 42 (4), 579-585 (2011)

[19] Kumar, S., Sloan, I.H. “A new collection-type method for Hammerstein integral equations.” J.Math.Comput. 48, 125-129 (1987)

[20] Alpert, B., Beylkin, G., Gines, D., Vozovoi, L. “Adaptive Solution Partial Differential Equations in Multiwavelet Bases.” J.Comp.Phys. 182, 149-190 (2002)

[21] Wazwaz, A.M. “A new method for solving singular initial value problems in the second-order ordinary differential equations.” Appl. Math. Comput. 128, 45-57 (2002)

[22] Avudainay agarn, A., Vano, C. “Wavelet-Galerkin method for integro-differential equations.” Appl.Numer.Math. 32, 247-254 (2000)

[23] Mohammadi, F., Hosseini, M.M. “Legendre wavelet method for solving linear stiff systems.” J. Adv. Res. Differential Equations. 2 (1), 47--57 (2010)

[24] Zheng Xiaoyang, Yang Xiaofan, Su Hong, Qiu, Liqiong “Discontinuous Legendre wavelet element method for elliptic partial differential equations.” Applied Mathematics and Computation. 218, 3002-3018 (2011)

[25] Vidden Chad, Yan, Jue “A new direct discontinuous Galerkin method with symmetric structure for nonlinear diffusion equations.” Journal of Computational Mathematics. Vol.31, No.6, 638-662 (2013)