• E-ISSN:

    2454-9584

    P-ISSN

    2454-8111

    Impact Factor 2021

    5.610

    Impact Factor 2022

    6.247

  • E-ISSN:

    2454-9584

    P-ISSN

    2454-8111

    Impact Factor 2021

    5.610

    Impact Factor 2022

    6.247

  • E-ISSN:

    2454-9584

    P-ISSN

    2454-8111

    Impact Factor 2021

    5.610

    Impact Factor 2022

    6.247

INTERNATIONAL JOURNAL OF INVENTIONS IN ENGINEERING & SCIENCE TECHNOLOGY

International Peer Reviewed (Refereed), Open Access Research Journal
(By Aryavart International University, India)

Paper Details

SOLVING THE K(2,2) EQUATION BY MEANS OF THE Q-HOMOTOPY ANALYSIS METHOD (Q-HAM)

Shaheed N Huseen

Thi-Qar University, Faculty of Computer Science and Mathematics, Mathematics Department, Thi-Qar, Iraq

6 - 19 Vol. 1, Jan-Dec, 2015
Receiving Date: 2014-12-28;    Acceptance Date: 0215-01-16;    Publication Date: 2015-01-22
Download PDF

Abstract

By means of the q-homotopy analysis method (q-HAM), the solution of the K(2,2) equation was obtained in this paper. Comparison of q- HAM with the Homotopy analysis method (HAM) and the Homotopy perturbation method (HPM) are made, The results reveal that the q-HAM has more accuracy than the others.

Keywords: q-Homotopy Analysis Method (q-HAM); K(2,2) equation

    References

  1. Abbasbandi S., Babolian E. and Ashtiani M., Numerical solution of the generalized Zakharov equation by Homotopy analysis method, Commun. Nonlinear Sci. Numer. Simulat.,14, (2009), 4114-4121.
  2. Adomian G., “A review of the decomposition method in applied mathematics,” Journal of Mathematical Analysis and Applications, vol. 135, no. 2, pp. 501–544, 1988.
  3. Alomari A. K., Noorani M.S.M. and Nazar R .' The homotopy analysis method for the exact solutions of the K(2,2), Burgers and coupled Burgers equations '. Appl. Math. Sci.Vol. 2, pp. 1963-1977, (2008)
  4. Ayub M., Rasheed A. and Hayat T., Exact flow of a third grade fluid past a porous plate using homotopy analysis method, Int. J. Eng. Sci. 41 (2003) 2091–2103
  5. Babolian E. and Saeidian J., Analytic approximate Solution to Burgers, Fisher, Huxley equations and two combined forms of these equations, Commun. Nonlinear Sci. Numer. Simulat.14, (2009), 1984-1992.
  6. El-Tawil M. A. and Huseen S.N., The q-Homotopy Analysis Method (q-HAM), International Journal of Applied mathematics and mechanics, 8 (15): 51-75, 2012.
  7. El-Tawil M. A. and Huseen S.N., On Convergence of The q-Homotopy Analysis Method, Int. J. Contemp. Math. Sciences, Vol. 8, 2013, no. 10, 481 – 497.
  8. Hayat T., Khan M. and Ayub M., On the explicit analytic solutions of an Oldroyd 6- constant fluid, Int. J. Engng. Sci. 42 (2004) 123–135.
  9. Hayat T., Khan M., Asghar S., Homotopy analysis of MHD flows of an Oldroyd 8- constant fluid, Acta Mech. 168 (2004) 213–232
  10. Hayat T., Khan M., Asghar S., Magneto hydrodynamic flow of an Oldroyd 6-constant fluid,Appl. Math. Comput. 155 (2004) 417–425.
  11. He J.H., Homotopy perturbation technique, Comp. Math. Appl. Mech. Eng., 178, (1999), 257-262.
  12. Huseen S. N. and Grace S. R. 2013, Approximate Solutions of Nonlinear Partial Differential Equations by Modified q-Homotopy Analysis Method (mq-HAM), Hindawi Publishing Corporation, Journal of Applied Mathematics, Article ID 569674, 9 pages http:// dx.doi.org/10.1155/ 2013/ 569674.
  13. Huseen S. N., Grace S. R. and El-Tawil M. A. 2013, The Optimal q-Homotopy Analysis Method (Oq-HAM), International Journal of Computers & Technology, Vol 11, No. 8.
  14. Iyiola O. S. 2013, q-Homotopy Analysis Method and Application to Fingero-Imbibition phenomena in double phase flow through porous media, Asian Journal of Current Engineering and Maths 2: 283 - 286.
  15. Iyiola O. S. 2013, A Numerical Study of Ito Equation and Sawada-Kotera Equation Both of Time-Fractional Type, Advances in Mathematics: Scientific Journal 2 , no.2, 71-79.
  16. Iyiola O. S., Soh M. E. and Enyi C. D. 2013, Generalized Homotopy Analysis Method (q-HAM) For Solving Foam Drainage Equation of Time Fractional Type, Mathematics in Engineering, Science & Aerospace (MESA), Vol. 4, Issue 4, p. 429-440.
  17. Iyiola O. S., Ojo, G. O. and Audu, J. D., A Comparison Results of Some Analytical Solutions of Model in Double Phase Flow through Porous Media, Journal of Mathematics and System Science 4 (2014) 275-284.
  18. Liao S.J., proposed Homotopy analysis technique for the solution of nonlinear problems,Ph.D Dissertation, Shanghai Jiao Tong University,1992.
  19. Liao S.J., Comparison between the homotopy analysis method and homotopy perturbation method, Applied Mathematics and Computation 169, 2005, 1186–1194
  20. Liao S.J., Notes on the Homotopy analysis method:Some difinitions and theorems,Commun. Nonlinear Sci. Numer. Simulat., 14, (2009), 983-997
  21. Lyapunov A.M., General problem on stability of motion, Taylor and Francis,1992 (English translation), 1982
  22. Maleknejad K. and Hadizade M., A new computational method for Volterra-Fredholm integral equations, Comput. Math. Appl., 37, (1999), 1-8.
  23. Onyejek O.N., Solutions of some parabolic inverse problems by homotopy analysis method, International Journal of Applied Mathematical Research, 3(1) (2014).
  24. Rosenau P., Hyman JM. Compactons: Solitons with finite wavelength. Phys Rev Lett1993; 70:564-567.
  25. Wazwaz A.M. and El-Sayed S. M., “A new modification of the Adomian decomposition method for linear and nonlinear operators,” Applied Mathematics and Computation, vol. 122, no. 3, pp. 393–405, 2001
  26. Wu Y.Y. and Liao S.J., Solving the one-loop soliton solution of the Vakhnenko equation by means of the homotopy analysis method, Chaos Solitons and Fractals 23 (5) (2004) 1733– 1740.
  27. Wu W., Liao S.J., Solvingsolitary waves with discontinuity by means of the homotopy analysis method, Chaos, Solitons and Fractals 23 (2004) 1733–1740.
  28. Yousefi S.A., Lotfi A. and Dehghan M., He’s Variational iteration method for solving nonlinear mixed Volterra-Fredholm integral equations, Computer and Mathematic with applications,58, (2009), 2172-2176.
Back