About this Journal Submit a Manuscript Table of Contents
Journal of Applied Mathematics
Volume 2013 (2013), Article ID 634670, 9 pages
http://dx.doi.org/10.1155/2013/634670
Research Article

Convergence of Variational Iteration Method for Second-Order Delay Differential Equations

Hunan Key Laboratory for Computation and Simulation in Science and Engineering and Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education, Xiangtan University, Xiangtan, Hunan 411105, China

Received 24 October 2012; Revised 17 December 2012; Accepted 17 December 2012

Academic Editor: Changbum Chun

Copyright © 2013 Hongliang Liu 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. Y. Xu, J. J. Zhao, and M. Z. Liu, “TH-stability of θ-method for a second-order delay differential equation,” Mathematica Numerica Sinica, vol. 26, no. 2, pp. 189–192, 2004. View at MathSciNet
  2. C. M. Huang and W. H. Li, “Delay-dependent stability analysis of the trapezium rule for a class of second-order delay differential equations,” Mathematica Numerica Sinica, vol. 29, no. 2, pp. 155–162, 2007. View at Zentralblatt MATH · View at MathSciNet
  3. X. H. Ding, J. Y. Zou, and M. Z. Liu, “P-stability of continuous Runge-Kutta-Nyström method for a class of delayed second order differential equations,” Numerical Mathematics, vol. 27, no. 2, pp. 123–132, 2005. View at MathSciNet
  4. J.-H. He, “Variational iteration method: a kind of non-linear analytical technique: some examples,” International Journal of Non-Linear Mechanics, vol. 34, no. 4, pp. 699–708, 1999. View at Publisher · View at Google Scholar · View at Scopus
  5. J.-H. He, “Some asymptotic methods for strongly nonlinear equations,” International Journal of Modern Physics B, vol. 20, no. 10, pp. 1141–1199, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. J.-H. He, “Variational iteration method for autonomous ordinary differential systems,” Applied Mathematics and Computation, vol. 114, no. 2-3, pp. 115–123, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. Z.-H. Yu, “Variational iteration method for solving the multi-pantograph delay equation,” Physics Letters A, vol. 372, no. 43, pp. 6475–6479, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. L. Xu, “Variational iteration method for solving integral equations,” Computers & Mathematics with Applications, vol. 54, no. 7-8, pp. 1071–1078, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. S.-P. Yang and A.-G. Xiao, “Convergence of the variational iteration method for solving multi-delay differential equations,” Computers & Mathematics with Applications, vol. 61, no. 8, pp. 2148–2151, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. S. Yang, A. Xiao, and H. Su, “Convergence of the variational iteration method for solving multi-order fractional differential equations,” Computers & Mathematics with Applications, vol. 60, no. 10, pp. 2871–2879, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. Y. Zhao and A. Xiao, “Variational iteration method for singular perturbation initial value problems,” Computer Physics Communications, vol. 181, no. 5, pp. 947–956, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. H. Liu, A. Xiao, and Y. Zhao, “Variational iteration method for delay differential-algebraic equations,” Mathematical & Computational Applications, vol. 15, no. 5, pp. 834–839, 2010. View at MathSciNet
  13. M. Rafei, D. D. Ganji, H. Daniali, and H. Pashaei, “The variational iteration method for nonlinear oscillators with discontinuities,” Journal of Sound and Vibration, vol. 305, no. 4-5, pp. 614–620, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. V. Marinca, N. Herişanu, and C. Bota, “Application of the variational iteration method to some nonlinear one-dimensional oscillations,” Meccanica, vol. 43, no. 1, pp. 75–79, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  15. M. Tatari and M. Dehghan, “On the convergence of He's variational iteration method,” Journal of Computational and Applied Mathematics, vol. 207, no. 1, pp. 121–128, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. J.-H. He and X.-H. Wu, “Variational iteration method: new development and applications,” Computers & Mathematics with Applications, vol. 54, no. 7-8, pp. 881–894, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. J.-H. He, “Variational iteration method—some recent results and new interpretations,” Journal of Computational and Applied Mathematics, vol. 207, no. 1, pp. 3–17, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. J.-H. He, “A short remark on fractional variational iteration method,” Physics Letters A, vol. 375, no. 38, pp. 3362–3364, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  19. J.-H. He, “Asymptotic methods for solitary solutions and compactons,” Abstract and Applied Analysis, vol. 2012, Article ID 916793, 130 pages, 2012. View at Publisher · View at Google Scholar