Solving the Kuramoto-Sivashinsky equation via Variational Iteration Method

  • Authors

    • majeed Ahmed Yousif Numerical Analysis-PDEs.
    • Saad A. Manaa
    • Fadhil H. Easif
    2014-07-08
    https://doi.org/10.14419/ijamr.v3i3.2901

  • Abstract

    In this study, the approximate solutions for the Kuramoto-Sivashinsky equation by using the Variational Iteration Method (VIM) are obtained. Comparisons with the exact solutions and the solutions obtained by the Homotopy Perturbation Method (HPM), the numerical example show that the Variational Iteration Method (VIM) is accurate and effective and suitable for this kind of problem.

    Keywords: Kuramoto-Sivashinsky equation, Variational Iteration Method.

  • References

    1. A. M. Wazwaz, Partial Differential Equations and Solitary Waves Theory, Springer, (2009).
    2. J. H. He,”A new approach to nonlinear partial differential equations”, Communications in Nonlinear Science and Numerical Simulation, 2, (1997), pp. 230-235.
    3. M. Safari, D. D. Ganji,” Application of He’s variational iteration method and Adomian’s decomposition method to the fractional, KdV–Burgers–Kuramoto equation”, Computers and Mathematics with Applications, 58, (2009), pp. 2091-2097.
    4. J. Biazar, H. Ghazvini,” He’s variational iteration method for fourth-order parabolic equations”, Computers and Mathematics with Applications, 54, (2007), pp.1047–1054.
    5. J. H. He,” Variational iteration method for delay differential equations”, Communications in Nonlinear Science and Numerical Simulation, 2, (1997), pp. 236-237.
    6. Y. Kuramoto, “Diffusion-induced chaos in reaction systems”, Suppl. Prog. Theor. Phys, 64, (1978), pp. 346-367.
    7. G. I. Sivashinsky, “Nonlinear analysis of hydrodynamic instability in laminar flames I: Derivation of basic equations”, Acta Astronau, 4, (1977), pp. 1177-1206.
    8. M. Krstic, Boundary control of PDEs: A Course on Backstepping Designs,Philadelphia: Society for Industrial and Applied Mathematics, 2008, chapter 10.
    9. Z. Shengtao, X. Chengkang, L. Guoping,” Output-feedback Stabilization of the Kuramoto-Sivashinsky-like Equation”, The 30th Chinese Control Conference, (2011), pp. 1015-1020.
    10. A. M. Wazwaz, “New solitary wave solutions to the Kuramoto-Sivashinsky and the Kawahara equations”, Applied Mathematics and Computation, 182, (2006), pp. 1642–1650.
    11. G. CH. Wu, “Challenge in the Variational iteration method -A new approach to identification of the Lagrange multipliers”, Journal of King Saud University, 25, (2013), pp. 175-178.
    12. A. Kassam, L. Trefethen, “Fourth-Order Time-Stepping for Stiff PDEs”, SIAM J. SCI. COMPUT. , 26, (2005), pp. 1214–1233.
    13. F. H. Easif, S. A. Manaa, Majeed A. Yousif, “The Homotopy Perturbation Method for Solving the Kuramoto-Sivashinsky equation”, IOSR Journal of Engineering, 3,(2013), pp. 22-27.

  • Downloads

  • How to Cite

    Yousif, majeed A., Manaa, S. A., & Easif, F. H. (2014). Solving the Kuramoto-Sivashinsky equation via Variational Iteration Method. International Journal of Applied Mathematical Research, 3(3), 260-264. https://doi.org/10.14419/ijamr.v3i3.2901

    Received date: 2014-05-22

    Accepted date: 2014-06-21

    Published date: 2014-07-08