- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Journal of Applied Mathematics
Volume 2012 (2012), Article ID 163821, 16 pages
A Coupled Method of Laplace Transform and Legendre Wavelets for Lane-Emden-Type Differential Equations
1College of Computer, National University of Defense Technology, Changsha 410073, China
2China Aerodynamics Research and Development Center, Sichuan, Mianyang 621000, China
Received 4 September 2012; Revised 11 October 2012; Accepted 15 October 2012
Academic Editor: Sazzad H. Chowdhury
Copyright © 2012 Fukang Yin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- S. Chandrasekhar, An Introduction to the Study of Stellar Structure, Dover, New York, NY, USA, 1967.
- H. T. Davis, Introduction to Nonlinear Differential and Integral Equations, Dover, New York, NY, USA, 1962.
- O. U. Richardson, The Emission of Electricity From Hot Bodies, Zongmans Green and Company, London, UK, 1921.
- N. T. Shawagfeh, “Nonperturbative approximate solution for Lane-Emden equation,” Journal of Mathematical Physics, vol. 34, no. 9, pp. 4364–4369, 1993.
- A.-M. Wazwaz, “A new algorithm for solving differential equations of Lane-Emden type,” Applied Mathematics and Computation, vol. 118, no. 2-3, pp. 287–310, 2001.
- A.-M. Wazwaz, “A new method for solving singular initial value problems in the second-order ordinary differential equations,” Applied Mathematics and Computation, vol. 128, no. 1, pp. 45–57, 2002.
- F. Olga and Š. Zdeněk, “A domian decomposition method for certain singular initial value problems,” Journal of Applied Mathematics, vol. 3, no. 2, pp. 91–98, 2010.
- J. I. Ramos, “Series approach to the Lane-Emden equation and comparison with the homotopy perturbation method,” Chaos, Solitons and Fractals, vol. 38, no. 2, pp. 400–408, 2008.
- A. Yildirim and T. Öziş, “Solutions of singular IVP's of Lane-Emden type by homotopy pertutbation method,” Physics Letters A, vol. 369, pp. 70–76, 2007.
- M. S. H. Chowdhury and I. Hashim, “Solutions of a class of singular second-order IVPs by homotopy-perturbation method,” Physics Letters A, vol. 365, no. 5-6, pp. 439–447, 2007.
- J.-H. He, “Variational approach to the Lane-Emden equation,” Applied Mathematics and Computation, vol. 143, no. 2-3, pp. 539–541, 2003.
- M. Dehghan and F. Shakeri, “Approximate solution of a differential equation arising in astrophysics using the variational iteration method,” New Astronomy, vol. 13, no. 1, pp. 53–59, 2008.
- A. Yildirım and T. Öziş, “Solutions of singular IVPs of Lane-Emden type by the variational iteration method,” Nonlinear Analysis, vol. 70, no. 6, pp. 2480–2484, 2009.
- S. Liao, “A new analytic algorithm of Lane-Emden type equations,” Applied Mathematics and Computation, vol. 142, no. 1, pp. 1–16, 2003.
- A. S. Bataineh, M. S. M. Noorani, and I. Hashim, “Homotopy analysis method for singular IVPs of Emden-Fowler type,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 4, pp. 1121–1131, 2009.
- C. Mohan and A. R. Al-Bayaty, “Power-series solutions of the Lane-Emden equation,” Astrophysics and Space Science, vol. 73, no. 1, pp. 227–239, 1980.
- V. S. Ertürk, “Differential transformation method for solving differential equations of Lane-Emden type,” Mathematical & Computational Applications, vol. 12, no. 3, pp. 135–139, 2007.
- S. Mukherjee, B. Roy, and P. K. Chaterjee, “Solution of Lane-Emden equation by differential transform method,” International Journal of Nonlinear Science, vol. 12, no. 4, pp. 478–484, 2011.
- K. Parand and M. Razzaghi, “Rational legendre approximation for solving some physical problems on semi-infinite intervals,” Physica Scripta, vol. 69, no. 5, pp. 353–357, 2004.
- K. Parand and A. Pirkhedri, “Sinc-Collocation method for solving astrophysics equations,” New Astronomy, vol. 15, no. 6, pp. 533–537, 2010.
- K. Parand, A. R. Rezaei, and A. Taghavi, “Lagrangian method for solving Lane-Emden type equation arising in astrophysics on semi-infinite domains,” Acta Astronautica, vol. 67, no. 7-8, pp. 673–680, 2010.
- S. S. Motsa and P. Sibanda, “A new algorithm for solving singular IVPs of Lane-Emden type,” in Proceedings of the 4th International Conference on Applied Mathematics, Simulation, Modelling (ASM '10), pp. 176–180, NAUN International Conferences, Corfu Island, Greece, July 2010.
- S. Karimi Vanani and A. Aminataei, “On the numerical solution of differential equations of Lane-Emden type,” Computers & Mathematics with Applications, vol. 59, no. 8, pp. 2815–2820, 2010.
- C. Yang and J. Hou, “A numerical method for Lane-Emden equations using hybrid functions and the collocation method,” Journal of Applied Mathematics, vol. 2012, Article ID 316534, 9 pages, 2012.
- S. A. Yousefi, “Legendre wavelets method for solving differential equations of Lane-Emden type,” Applied Mathematics and Computation, vol. 181, no. 2, pp. 1417–1422, 2006.
- R. K. Pandey, N. Kumar, A. Bhardwaj, and G. Dutta, “Solution of Lane-Emden type equations using legendre operational matrix of differentiation,” Applied Mathematics and Computation, vol. 218, no. 14, pp. 7629–7637, 2012.
- J. P. Boyd, “Chebyshev spectral methods and the Lane-Emden problem,” Numerical Mathematics, vol. 4, no. 2, pp. 142–157, 2011.
- S. A. Khuri, “A Laplace decomposition algorithm applied to a class of nonlinear differential equations,” Journal of Applied Mathematics, vol. 1, no. 4, pp. 141–155, 2001.
- Y. Khan, “An effective modification of the laplace decomposition method for nonlinear equations,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 10, no. 11-12, pp. 1373–1376, 2009.
- M. Khan and M. A. Gondal, “A new analytical solution of foam drainage equation by laplace decomposition method,” Journal of Advanced Research in Scientific Computing, vol. 2, no. 2, pp. 53–64, 2010.
- S. Abbasbandy, “Application of He's homotopy perturbation method for Laplace transform,” Chaos, Solitons and Fractals, vol. 30, no. 5, pp. 1206–1212, 2006.
- S. A. Khuri and A. Sayfy, “A laplace variational iteration strategy for the solution of differential equations,” Applied Mathematics Letters, vol. 25, no. 12, pp. 2298–2305, 2012.
- M. Madani and M. Fathizadeh, “Homotopy perturbation algorithm using laplace transformation,” Nonlinear Science Letters A, vol. 1, pp. 263–267, 2010.
- M. Khan, M. A. Gondal, and S. Karimi Vanani, “On the coupling of homotopy perturbation and laplace transformation for system of partial differential equations,” Applied Mathematical Sciences, vol. 6, no. 9–12, pp. 467–478, 2012.
- M. Madani, M. Fathizadeh, Y. Khan, and A. Yildirim, “On the coupling of the homotopy perturbation method and laplace transformation,” Mathematical and Computer Modelling, vol. 53, no. 9-10, pp. 1937–1945, 2011.
- Y. Khan and Q. Wu, “Homotopy perturbation transform method for nonlinear equations using He's polynomials,” Computers & Mathematics with Applications, vol. 61, no. 8, pp. 1963–1967, 2011.
- V. G. Gupta and S. Gupta, “Homotopy perturbation transform method for solving initial boundary value problems of variable coefficients,” International Journal of Nonlinear Science, vol. 12, no. 3, pp. 270–277, 2011.
- J. Singh, D. Kumar, and S. Rathore, “Application of homotopy perturbation transform method for solving linear and nonlinear Klein-Gordon equations,” Journal of Information and Computing Science, vol. 7, pp. 131–139, 2012.