2016 Volume 6 Issue 3
Article Contents

Amit Prakash, Manoj Kumar. HE'S VARIATIONAL ITERATION METHOD FOR THE SOLUTION OF NONLINEAR NEWELL-WHITEHEAD-SEGEL EQUATION[J]. Journal of Applied Analysis & Computation, 2016, 6(3): 738-748. doi: 10.11948/2016048
Citation: Amit Prakash, Manoj Kumar. HE'S VARIATIONAL ITERATION METHOD FOR THE SOLUTION OF NONLINEAR NEWELL-WHITEHEAD-SEGEL EQUATION[J]. Journal of Applied Analysis & Computation, 2016, 6(3): 738-748. doi: 10.11948/2016048

HE'S VARIATIONAL ITERATION METHOD FOR THE SOLUTION OF NONLINEAR NEWELL-WHITEHEAD-SEGEL EQUATION

  • In this paper, we apply He's Variational iteration method (VIM) for solving nonlinear Newell-Whitehead-Segel equation. By using this method three different cases of Newell-Whitehead-Segel equation have been discussed. Comparison of the obtained result with exact solutions shows that the method used is an effective and highly promising method for solving different cases of nonlinear Newell-Whitehead-Segel equation.
    MSC: 44A99;35Q99
  • 加载中
  • [1] R. Ezzati and K. Shakibi, Using adomians decomposition and multi-quadric quasi-interpolation methods for solving Newell-Whitehead equation, Procedia Computer Science, 3(2011), 1043-1048.

    Google Scholar

    [2] J. H. He, Variational iteration method for delay differential equations, Communications in Nonlinear Science and Numerical Simulation, 2(1997), 235-236.

    Google Scholar

    [3] J. H. He, An approximate solution technique depending on an artificial parameter:A special example, Communications in Nonlinear Science and Numerical Simulation, 3(1998), 92-97.

    Google Scholar

    [4] J. H. He, Variational iteration method a kind of non-linear analytical technique:some examples, International Journal of Non-Linear Mechanics, 34(1999), 699-708.

    Google Scholar

    [5] J. H. He, Y.Q. Wan and Q. Guo, An iteration formulation for normalized diode characteristics, International Journal of Circuit Theory and Applications, 32(2004), 629-632.

    Google Scholar

    [6] J. H. He, Some asymptotic methods for strongly nonlinear equations, International Journal of Modern Physics B, 20(2006), 1141.

    Google Scholar

    [7] J. H. He, Non-perturbative Methods for Strongly Nonlinear Problems, dissertation.de-Verlag im Internet GmbH, Berlin, 2006.

    Google Scholar

    [8] J. H. He, Approximate analytical solution for seepage flow with fractional derivatives in porous media, Computer Methods in Applied Mechanics and Engineering, 167(1998), 57-68.

    Google Scholar

    [9] J. H. He, Approximate solution of nonlinear differential equations with convolution product nonlinearities, Computer Methods in Applied Mechanics and Engineering, 167(1998), 69-73.

    Google Scholar

    [10] J. H. He, Homotopy perturbation technique, Computer Methods in Applied Mechanics and Engineering, 178(1999), 257-262.

    Google Scholar

    [11] J. H. He, A coupling method of a homotopy technique and a perturbation technique for non-linear problems, International Journal of Non-Linear Mechanics, 35(2000), 37-43.

    Google Scholar

    [12] J. H. He, Application of homotopy perturbation method to nonlinear wave equations, Chaos Solitons & Fractals, 26(2005), 695-700.

    Google Scholar

    [13] J. H. He, Homotopy perturbation method for bifurcation of nonlinear problems, International Journal of Nonlinear Sciences and Numerical Simulation, 6(2005), 207-208.

    Google Scholar

    [14] J. H. He, Nonlinear variants of the BBM equation with compact and noncompact physical structures, Phys. Lett. A, 26(2005), 695.

    Google Scholar

    [15] J. H. He, Periodic solutions and bifurcations of delay-differential equations, International Journal of Nonlinear Sciences and Numerical Simulation, 347(2005), 228-230.

    Google Scholar

    [16] J. H. He, Construction of solitary solution and compaction-like solution by variational iteration method, Chaos Solitons Fractals, 29(2006), 108-113.

    Google Scholar

    [17] J. H. He, Homotopy perturbation method for solving boundary value problems, Phys. Lett., A, 350(2006), 87-88.

    Google Scholar

    [18] J. H. He, Some asymptotic methods for strongly nonlinear equations, Int. J. Mod. Phys. B, 20(2006), 41.

    Google Scholar

    [19] H. Koçak, A. Yildirimm, D.H. Zhang, and S.T. Mohyud-Din, The comparative Boubaker polynomials expansion scheme and homotopy perturbation method for solving a standard non-linear second-order boundary value problem, Mathematical and Computer Modelling, 54(2011), 417-422.

    Google Scholar

    [20] S. S. Nourazar, M. Soori and A. Nazari-Golshan, On The exact solution of Newell-Whitehead-Segel equation using the Homotopy perturbation method, Australian Journal of Basic and Applied Sciences & Fractals, 5(2011)(8), 1400-1411.

    Google Scholar

    [21] A. M. Wazwaz, Partial Differential Equations and Solitary Waves Theory, Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg, 2009.

    Google Scholar

    [22] A. Yildirim, Homotopy perturbation method for the mixed Volterra-Fredholm integral equations, Chaos Solitons & Fractals, 42(2009), 2760-2764.

    Google Scholar

Article Metrics

Article views(3083) PDF downloads(1217) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint