Table of Contents
International Journal of Partial Differential Equations
Volume 2013 (2013), Article ID 846749, 7 pages
http://dx.doi.org/10.1155/2013/846749
Research Article

Numerical Approximation for Nonlinear Gas Dynamic Equation

Department of Applied Mathematics, School of Mathematical Sciences, University of Guilan, P.O. Box 41335-1914, Rasht, Iran

Received 15 March 2013; Revised 25 May 2013; Accepted 28 May 2013

Academic Editor: Zhenhua Guo

Copyright © 2013 Hossein Aminikhah and Ali Jamalian. 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. H. Nayfeh, Introduction to Perturbation Techniques, Wiley-Interscience, New York, NY, USA, 1981.
  2. J.-H. He, “Homotopy perturbation technique,” Computer Methods in Applied Mechanics and Engineering, vol. 178, no. 3-4, pp. 257–262, 1999. View at Publisher · View at Google Scholar
  3. J.-H. He, “Coupling method of a homotopy technique and a perturbation technique for non-linear problems,” International Journal of Non-Linear Mechanics, vol. 35, no. 1, pp. 37–43, 2000. View at Publisher · View at Google Scholar · View at Scopus
  4. J.-H. He, “Addendum: new interpretation of homotopy perturbation method,” International Journal of Modern Physics B, vol. 20, no. 18, pp. 2561–2568, 2006. View at Publisher · View at Google Scholar · View at Scopus
  5. J.-H. He, “Recent development of the homotopy perturbation method,” Topological Methods in Nonlinear Analysis, vol. 31, no. 2, pp. 205–209, 2008. View at Google Scholar
  6. J.-H. He, “The homotopy perturbation method for nonlinear oscillators with discontinuities,” Applied Mathematics and Computation, vol. 151, no. 1, pp. 287–292, 2004. View at Publisher · View at Google Scholar · View at Scopus
  7. J.-H. He, “Application of homotopy perturbation method to nonlinear wave equations,” Chaos, Solitons and Fractals, vol. 26, no. 3, pp. 695–700, 2005. View at Publisher · View at Google Scholar · View at Scopus
  8. J.-H. He, “Limit cycle and bifurcation of nonlinear problems,” Chaos, Solitons and Fractals, vol. 26, no. 3, pp. 827–833, 2005. View at Publisher · View at Google Scholar · View at Scopus
  9. A. Rajabi, D. D. Ganji, and H. Taherian, “Application of homotopy perturbation method in nonlinear heat conduction and convection equations,” Physics Letters A, vol. 360, no. 4-5, pp. 570–573, 2007. View at Publisher · View at Google Scholar · View at Scopus
  10. D. D. Ganji and A. Sadighi, “Application of homotopy-perturbation and variational iteration methods to nonlinear heat transfer and porous media equations,” Journal of Computational and Applied Mathematics, vol. 207, no. 1, pp. 24–34, 2007. View at Publisher · View at Google Scholar · View at Scopus
  11. D. D. Ganji, “The application of He's homotopy perturbation method to nonlinear equations arising in heat transfer,” Physics Letters A, vol. 355, no. 4-5, pp. 337–341, 2006. View at Publisher · View at Google Scholar · View at Scopus
  12. S. Abbasbandy, “A numerical solution of Blasius equation by Adomian's decomposition method and comparison with homotopy perturbation method,” Chaos, Solitons and Fractals, vol. 31, no. 1, pp. 257–260, 2007. View at Publisher · View at Google Scholar · View at Scopus
  13. J. Biazar and H. Ghazvini, “Exact solutions for non-linear Schrödinger equations by He's homotopy perturbation method,” Physics Letters A, vol. 366, no. 1-2, pp. 79–84, 2007. View at Publisher · View at Google Scholar
  14. S. Abbasbandy, “Numerical solutions of the integral equations: homotopy perturbation method and Adomian's decomposition method,” Applied Mathematics and Computation, vol. 173, no. 1, pp. 493–500, 2006. View at Publisher · View at Google Scholar · View at Scopus
  15. J.-H. He, “Homotopy perturbation method for solving boundary value problems,” Physics Letters A, vol. 350, no. 1-2, pp. 87–88, 2006. View at Publisher · View at Google Scholar · View at Scopus
  16. Q. Wang, “Homotopy perturbation method for fractional KdV-Burgers equation,” Chaos, Solitons and Fractals, vol. 35, no. 5, pp. 843–850, 2008. View at Publisher · View at Google Scholar
  17. E. Yusufoǧlu, “Homotopy perturbation method for solving a nonlinear system of second order boundary value problems,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 8, no. 3, pp. 353–358, 2007. View at Google Scholar · View at Scopus
  18. J. Biazar and B. Ghanbari, “The homotopy perturbation method for solving neutral functional-differential equations with proportional delays,” Journal of King Saud University, vol. 24, no. 1, pp. 33–37, 2012. View at Publisher · View at Google Scholar · View at Scopus
  19. D. J. Evans and H. Bulut, “A new approach to the gas dynamics equation: an application of the decomposition method,” International Journal of Computer Mathematics, vol. 79, no. 7, pp. 817–822, 2002. View at Publisher · View at Google Scholar · View at Scopus
  20. A. D. Polyanin and V. F. Zaitsev, Handbook of Nonlinear Partial Differential Equations, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2004.
  21. T. G. Elizarova, Quasi-Gas Dynamic Equations, Computational Fluid and Solid Mechanics, Springer, Dordrecht, The Netherlands, 2009. View at Publisher · View at Google Scholar
  22. H. Jafari, C. Chun, S. Seifi, and M. Saeidy, “Analytical solution for nonlinear gas dynamic equation by homotopy analysis method,” Applications and Applied Mathematics, vol. 4, no. 1, pp. 149–154, 2009. View at Google Scholar
  23. W. F. Ames, Nonlinear Partial Differential Equations in Engineering, Academic Press, New York, NY, USA, 1965.
  24. M. Rasulov and T. Karaguler, “Finite difference schemes for solving system equations of gas dynamic in a class of discontinuous functions,” Applied Mathematics and Computation, vol. 143, no. 1, pp. 145–164, 2003. View at Publisher · View at Google Scholar · View at Scopus
  25. H. Aminikhah and A. Jamalian, “An analytical approximation for boundary layer flow convection heat and mass transfer over a flat plate,” The Journal of Mathematics and Computer Science, vol. 5, no. 4, pp. 241–257, 2012. View at Google Scholar
  26. H. Aminikhah, F. Mehrdoust, and A. Jamalian, “A new efficient method for nonlinear Fisher-type equations,” Journal of Applied Mathematics, vol. 2012, Article ID 586454, 18 pages, 2012. View at Publisher · View at Google Scholar
  27. H. Aminikhah and A. Jamalian, “A new efficient method for solving the nonlinear Fokker-Planck equation,” Scientia Iranica, vol. 19, pp. 1133–1139, 2012. View at Google Scholar
  28. H. Aminikhah and M. Hemmatnezhad, “An efficient method for quadratic Riccati differential equation,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 4, pp. 835–839, 2010. View at Publisher · View at Google Scholar · View at Scopus