Iterative application method for solving system modified korteweg-de vries equations

  • Authors

    • Zeiad Y.Ali University of Mosul College of Physical Education and Sport Sciences
    • Allawee .
    2019-08-25
    https://doi.org/10.14419/ijet.v8i3.27020
  • Modified Korteweg-De Vries Equations Combined, A New Iterative Method (NIM).

  • Abstract

    In this paper we use a new iterative method (NIM) to solution the floating wave the new modified Korteweg-de Vries equations. We have shown that a more accurate NIM solution with modified Korteweg-de Vries equations is very efficient, convenient and completely accurate for nonlinear equations systems. The NIM solution is expected to find a wide-ranging application in engineering or physics. The results also show that the NIM solution is more reliable and easy to compute and compute speed than HPM and He’s Method (NIM) is introduced to overcome the difficulty arising in calculating Adomian polynomials.

     

     

    Author Biography

    • Zeiad Y.Ali, University of Mosul College of Physical Education and Sport Sciences

      Assistant lecturer

      University of Mosul College of Physical Education and Sport Sciences


  • References

    1. [1] D.J. Korteweg, G. de Vries, On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary wave, Philos. Mag. Vol.39, 1895, pp. 422–443. https://doi.org/10.1080/14786449508620739.

      [2] Luwai Wazzan, A modified tanh–coth method for solving the KdV an d the KdV–Burgers equations, Journal of Communication in nonlinearscience and numerical simulation, (2007)

      [3] A.J. Khattak, Siraj-ul-Islam, A comparative study of numerical solutions of a class of KdV equation, Journal of Computnational Applied Mathematical, Vol. 199, 2008, pp.425–434. https://doi.org/10.1016/j.amc.2007.10.002.

      [4] T. Ozis, S. Ozer S, A simple similarity-transformation-iterative scheme applied to Korteweg-de Vries equation, Journal of Applied Mathematical Compution, Vol. 173, 2006, pp.19–32. https://doi.org/10.1016/j.amc.2005.02.059.

      [5] S. F. Deng, Chaos, Solitons and Fractals 25, 475 (2005). https://doi.org/10.1016/j.chaos.2004.11.019.

      [6] G. Tsigaridas, A. Fragos, I. Polyzos, M. Fakis, A. Ioannou, V. Giannetas, and P. Persephonis, Chaos, Solitons and Fractals 23, 1841 (2005). https://doi.org/10.1016/S0960-0779(04)00449-7.

      [7] O. Pashaev and G. Tano˘glu, Chaos, Solitons and Fractals 26, 95 (2005). https://doi.org/10.1016/j.chaos.2004.12.021.

      [8] V.O. Vakhnenko, E. J. Parkes, and A. J. Morrison, Chaos, Solitons and Fractals 17, 683 (2003). https://doi.org/10.1016/S0960-0779(02)00483-6.

      [9] L. De-Sheng, G. Feng, and Z. Hong-Qing, Chaos, Solitons and Fractals 20, 1021 (2004). https://doi.org/10.1016/j.chaos.2003.09.006.

      [10] H.A. Abdusalam, Int. J. Nonlinear Sci. Numer. Simul. 6, 99 (2005).

      [11] T.A. Abassy, M.A. El-Tawil, and H.K. Saleh, Int. J. Nonlinear Sci. Numer. Simul. 5, 327 (2004). https://doi.org/10.1515/IJNSNS.2004.5.4.327.

      [12] D. Kaya and S.M. El-Sayed, Chaos, Solitons and Fractals 17, 869 (2003). https://doi.org/10.1016/S0960-0779(02)00569-6.

      [13] H. M. Liu, Chaos, Solitons and Fractals 23, 573 (2005). https://doi.org/10.1016/j.chaos.2004.05.005.

      [14] A. M. Meson and F. Vericat, Chaos, Solitons and Fractals 19, 1031 (2004). https://doi.org/10.1016/S0960-0779(03)00204-2.

      [15] J.H. He, Int. J. Nonlinear Mech. 34, 699 (1999). https://doi.org/10.1016/S0020-7462(98)00048-1.

      [16] G.-E. Draganescu and V. Capalnasan, Int. J. Nonlinear Sci. Numer. Simul. 4, 219 (2004). https://doi.org/10.1515/IJNSNS.2003.4.3.219.

      [17] J.H. He, Int. J. Nonlinear Mech. 37, 309 (2002). https://doi.org/10.1023/A:1016050922759.

      [18] H. M. Liu, Chaos, Solitons and Fractals 23, 577 (2005). https://doi.org/10.1016/j.chaos.2004.05.004.

      [19] G. Adomain, J. Math. Anal. Appl. 135, 501 (1988).

      [20] A. M. Wazwaz, Appl. Math. Comput. 92, 1 (1998). https://doi.org/10.1016/S0096-3003(97)10037-6.

      [21] Elsayed M. E. Zayed, Taher A. Nofal, and Khaled A. Gepreel, The Homotopy Perturbation Method for Solving Nonlinear Burgers and New Coupled Modified Korteweg-de Vries Equations, Z. Naturforsch. 63a, 627 – 633 (2008); received April 23, 2008. https://doi.org/10.1515/zna-2008-10-1103.

      [22] E. Fan, Phys. Lett. A 282, 18 (2001). https://doi.org/10.1016/S0375-9601(01)00161-X.

      [23] V. Daftardar-Gejji and H. Jafari, “An iterative method for solving nonlinear functional equationsâ€, Journal of Mathematical Analysis and Applications, vol. 316, no. 2, pp. 753-763, 2006. https://doi.org/10.1016/j.jmaa.2005.05.009.

      [24] A. A. Hemeda, “New iterative method: application to the nthorder integro-differential equationsâ€, Information B, vol. 16, no. 6, pp. 3841-3852, 2013. https://doi.org/10.1155/2013/617010.

      [25] G. Adomian, “Solving Frontier Problems of Physics: The Decomposition Methodâ€, Kluwer, 1994. https://doi.org/10.1007/978-94-015-8289-6.

      [26] J. H. He, “Homotopy perturbation techniqueâ€, Computer Methods in Applied Mechanics and Engineering, vol. 178, no. 3-4, pp. 257-262, 1999. https://doi.org/10.1016/S0045-7825(99)00018-3.

      [27] A. A. Hemeda, “Variational iteration method for solving nonlinear coupled equations in 2-dimensional space in fluid mechanicsâ€, International Journal of Contemporary Mathematical Sciences, vol. 7, no. 37, pp. 1839-1852, 2012.

      [28] Z.Y. A, Application New Iterative Method For Solving Nonlinear Burger’s Equation And Coupled Burger’s Equations ,University of Mosul, College of Physical Education and Sport Sciences Mosul, Nineveh 41002, Iraq, IJCSI International Journal of Computer Science Issues, Volume 15, Issue 3, May 2018.

      [29] Manoj Kumar, Anuj Shanker Saxena, NEW ITERATIVE METHOD FOR SOLVING HIGHER ORDER KDV EQUATIONS",4th international conference on science, technology and management , India tnternational Centre, New Delhi, (ICSTM-16), 15 May 2016, www.conferenceworld,in, Isbn;978-81-932074-8-2.

      [30] S. Bhalekar and V. Daftardar-Gejji. Convergence of the new iterative method. International Journal of Differential Equations, 2011, 2011. https://doi.org/10.1155/2011/989065.

      [31] J.H. He, Appl. Math. Comput. 151, 287 (2004). https://doi.org/10.1016/S0096-3003(03)00341-2.

  • Downloads

  • How to Cite

    Y.Ali, Z., & ., A. (2019). Iterative application method for solving system modified korteweg-de vries equations. International Journal of Engineering & Technology, 8(3), 188-192. https://doi.org/10.14419/ijet.v8i3.27020

    Received date: 2019-02-02

    Accepted date: 2019-06-12

    Published date: 2019-08-25