Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2014, Article ID 735831, 8 pages
http://dx.doi.org/10.1155/2014/735831
Research Article

Using an Effective Numerical Method for Solving a Class of Lane-Emden Equations

1Department of Mathematics, Inner Mongolia University of Technology, Hohhot 010051, China
2Jining Teachers College, Wūlánchábù, Inner Mongolia 012000, China

Received 26 March 2014; Revised 12 May 2014; Accepted 22 May 2014; Published 18 June 2014

Academic Editor: Igor Leite Freire

Copyright © 2014 Yulan Wang 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.

Linked References

  1. 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,” Applied Mathematics and Computation, vol. 219, no. 10, pp. 5004–5019, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. M. Dehghan, S. Aryanmehr, and M. R. Eslahchi, “A technique for the numerical solution of initial-value problems based on a class of Birkhoff-type interpolation method,” Journal of Computational and Applied Mathematics, vol. 244, pp. 125–139, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. K. Parand, M. Dehghan, A. R. Rezaei, and S. M. Ghaderi, “An approximation algorithm for the solution of the nonlinear Lane-Emden type equations arising in astrophysics using Hermite functions collocation method,” Computer Physics Communications, vol. 181, no. 6, pp. 1096–1108, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. C. Harley and E. Momoniat, “Instability of invariant boundary conditions of a generalized Lane-Emden equation of the second-kind,” Applied Mathematics and Computation, vol. 198, no. 2, pp. 621–633, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. E. Momoniat and C. Harley, “An implicit series solution for a boundary value problem modelling a thermal explosion,” Mathematical and Computer Modelling, vol. 53, no. 1-2, pp. 249–260, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. A.-M. Wazwaz, “The combined Laplace transform-Adomian decomposition method for handling nonlinear Volterra integro-differential equations,” Applied Mathematics and Computation, vol. 216, no. 4, pp. 1304–1309, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. J.-S. Duan, R. Rach, A.-M. Wazwaz, T. Chaolu, and Z. Wang, “A new modified Adomian decomposition method and its multistage form for solving nonlinear boundary value problems with Robin boundary conditions,” Applied Mathematical Modelling, vol. 37, no. 20-21, pp. 8687–8708, 2013. View at Publisher · View at Google Scholar · View at Scopus
  8. J. S. Duan, R. Rach, and A. Wazwaz, “Solution of the model of beam-type micro- and nano-scale electrostatic actuators by a new modified Adomian decomposition method for nonlinear boundary value problems,” International Journal of Non-Linear Mechanics, vol. 49, pp. 159–169, 2013. View at Publisher · View at Google Scholar · View at Scopus
  9. M. M. Al-Sawalha, M. S. M. Noorani, and I. Hashim, “Numerical experiments on the hyperchaotic Chen system by the Adomian decomposition method,” International Journal of Computational Methods, vol. 5, no. 3, pp. 403–412, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. S. Ghosh, A. Roy, and D. Roy, “An adaptation of Adomian decomposition for numeric-analytic integration of strongly nonlinear and chaotic oscillators,” Computer Methods in Applied Mechanics and Engineering, vol. 196, no. 4–6, pp. 1133–1153, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. A. Y. Al Bayati, A. J. AL Sawoor, and M. A. Samarji, “A multistage Adomian decomposition method for solving the autonomous Van Der Pol system,” Australian Journal of Basic and Applied Sciences, vol. 3, no. 4, pp. 4397–4407, 2009. View at Google Scholar · View at Scopus
  12. Y. L. Wang, X. J. Cao, and X. Li, “A new method for solving singular fourth-order boundary value problems with mixed boundary conditions,” Applied Mathematics and Computation, vol. 217, no. 18, pp. 7385–7390, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. Y. L. Wang, M. J. Du, F. Tan, Z. Li, and T. Nie, “Using reproducing kernel for solving a class of fractional partial differential equation with non-classical conditions,” Applied Mathematics and Computation, vol. 219, no. 11, pp. 5918–5925, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. Z. Li, Y. Wang, F. Tan, X. Wan, and T. Nie, “The solution of a class of singularly perturbed two-point boundary value problems by the iterative reproducing kernel method,” Abstract and Applied Analysis, vol. 2012, Article ID 984057, 7 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. Y. L. Wang, S. Lu, F. Tan, M. Du, and H. Yu, “Solving a class of singular fifth-order boundary value problems using reproducing kernel Hilbert space method,” Abstract and Applied Analysis, vol. 2013, Article ID 925192, 6 pages, 2013. View at Publisher · View at Google Scholar · View at Scopus
  16. Z. Y. Li, Y. L. Wang, and F. Tan, “The solution of a class of third-order boundary value problems by the reproducing kernel method,” Abstract and Applied Analysis, vol. 2012, Article ID 195310, 11 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. X. Y. Li, B. Y. Wu, and R. T. Wang, “Reproducing kernel method for fractional riccati differential equations,” Abstract and Applied Analysis, vol. 2014, Article ID 970967, 6 pages, 2014. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. F. Z. Geng and S. P. Qian, “Solving singularly perturbed multipantograph delay equations based on the reproducing kernel method,” Abstract and Applied Analysis, vol. 2014, Article ID 794716, 6 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  19. L.-H. Yang, H.-Y. Li, and J.-R. Wang, “Solving a system of linear Volterra integral equations using the modified reproducing kernel method,” Abstract and Applied Analysis, vol. 2013, Article ID 196308, 5 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  20. L. H. Yang and M. G. Cui, “New algorithm for a class of nonlinear integro-differential equations in the reproducing kernel space,” Applied Mathematics and Computation, vol. 174, no. 2, pp. 942–960, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. X. Q. Lv and M. G. Cui, “An efficient computational method for linear fifth-order two-point boundary value problems,” Journal of Computational and Applied Mathematics, vol. 234, no. 5, pp. 1551–1558, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. M. G. Cui and Z. Chen, “The exact solution of nonlinear age-structured population model,” Nonlinear Analysis: Real World Applications, vol. 8, no. 4, pp. 1096–1112, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. J. N. Niu, Y. Z. Lin, and M. G. Cui, “A novel approach to calculation of reproducing kernel on infinite interval and applications to boundary value problems,” Abstract and Applied Analysis, vol. 2013, Article ID 959346, 7 pages, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet