Ghasemi, M., Azizi, A., Fardi, M. (2010). Numerical solution of seven-order Sawada-Kotara equations by homotopy perturbation method. Theory of Approximation and Applications, 7(1), 69-77.

M. Ghasemi; A. Azizi; M. Fardi. "Numerical solution of seven-order Sawada-Kotara equations by homotopy perturbation method". Theory of Approximation and Applications, 7, 1, 2010, 69-77.

Ghasemi, M., Azizi, A., Fardi, M. (2010). 'Numerical solution of seven-order Sawada-Kotara equations by homotopy perturbation method', Theory of Approximation and Applications, 7(1), pp. 69-77.

Ghasemi, M., Azizi, A., Fardi, M. Numerical solution of seven-order Sawada-Kotara equations by homotopy perturbation method. Theory of Approximation and Applications, 2010; 7(1): 69-77.

Numerical solution of seven-order Sawada-Kotara equations by homotopy perturbation method

^{1}Department of Applied Mathematics, Faculty of Science, Shahrekord University, Shahrekord, P. O. Box 115, Iran.

^{2}Department of Mathematics, Sanandaj Branch, Islamic Azad University, Sanandaj, Iran.

^{3}Department of Mathematics, Islamic Azad University, Boroujen Branch, Boroujen, Iran.

Abstract

In this paper, an application of homotopy perturbation method is applied to nding the solutions of the seven-order Sawada-Kotera (sSK) and a Lax's seven-order KdV (LsKdV) equations. Then obtain the exact solitary-wave so- lutions and numerical solutions of the sSK and LsKdV equations for the initial conditions. The numerical solutions are compared with the known analytical solutions. Their remarkable accuracy are nally demonstrated for the both seven-order equations.

Article Title [Persian]

Numerical solution of seven-order Sawada-Kotara
equations by homotopy perturbation method

Authors [Persian]

M. Ghasemi^{1}; A. Azizi^{2}; M. Fardi^{3}

^{1}Department of Applied Mathematics, Faculty of Science, Shahrekord University, Shahrekord, P. O.
Box 115, Iran.

^{2}Department of Mathematics, Sanandaj Branch, Islamic Azad University, Sanandaj, Iran.

^{3}Department of Mathematics, Islamic Azad University, Boroujen Branch, Boroujen, Iran.

Abstract [Persian]

In this paper, an application of homotopy perturbation method is applied to nding the solutions of the seven-order Sawada-Kotera (sSK) and a Lax's seven-order KdV (LsKdV) equations. Then obtain the exact solitary-wave so- lutions and numerical solutions of the sSK and LsKdV equations for the initial conditions. The numerical solutions are compared with the known analytical solutions. Their remarkable accuracy are nally demonstrated for the both seven-order equations.

[1] M. Ghasemi, M. Tavassoli Kajani, Application of He's homotopy perturbation method for linear and nonlinear heat equations, Math. Scientic J. 1 (2008) 17-27. [2] M. Ghasemi, M. Tavassoli Kajani, A. Azizi, The application of homotopy pertur- bation method for solving Schrodinger equation, Math. Scientic J. 1 (5) (2009) 47-55. [3] M. Ghasemi, M. Tavassoli Kajani, A. Davari, Numerical solution of two- dimensional nonlinear dierential equation by homotopy perturbation method, Appl. Math. Comput. 189 (2007) 341-345. [4] M. Ghasemi, M. Tavassoli Kajani, E. Babolian, Numerical solutions of the non- linear Volterra-Fredholm integral equations by using Homotopy perturbation method, Appl. Math. Comput. 188 (2007) 446-449.

[5] M. Ghasemi, M. Tavassoli Kajani, E. Babolian, Application of He's homotopy perturbation method to nonlinear integro-dierential equations, Appl. Math. Comput. 188 (2007) 538-548. [6] M. Ghasemi, M. Tavassoli Kajani, Application of He's homotopy perturbation method to solve a diusion-convection problem, Math. Sci. Quarterly J. 4 (2010) 171-186. [7] M. Ghasemi, M. Tavassoli Kajani, R. Khoshsiar Ghaziani, Numerical solution of fth order KdV equations by homotopy perturbation method, Math. Sci. Quar- terly J. (2011) In Press. [8] S. Vahdati, Z. Abbas, M. Ghasemi, Application of Homotopy Analysis Method to Fredholm and Volterra integral equations, Math. Sci. Quarterly J. 4 (2010) 267-282. [9] J.H. He, Application of homotopy perturbation method to nonlinear wave equa- tions, Chaos Solitons & Fractals 26 (2005) 695-700. [10] J.H. He, Variational iteration method: a kind of nonlinear analytical technique: some examples, Int. J. Nonlinear Mech. 34 (1999) 699-708. [11] J.H. He, Homotopy perturbation technique, Comput. Methods Appl. Mech. En- gng. 178 (1999) 257-262. [12] J.H. He, Homotopy perturbation method: a new nonlinear analytical technique, Appl. Math. Comput. 135 (2003) 73-79. [13] J.H. He, A coupling method of homotopy technique and perturbation technique for nonlinear problems, Int. J. Nonlinear Mech. 35 (2000) 37-43. [14] J.H. He, A review on some new recently developed nonlinear analytical tech- niques, Int. J. Nonlinear Sci. Numer. Simul. 1 (2000) 51-70. [15] J.H. He, The homotopy perturbation method for nonlinear oscillators with dis- continuities, Appl. Math. Comput. 151 (2004) 287-292. [16] J.H. He, Comparison of homotopy perturbation method and homotopy analysis method, Appl. Math. Comput. 156 (2004) 527-539. [17] J.H. He, Bookkeeping parameter in perturbation methods, Int. J. Nonlinear Sci. Numer. Simul. 2 (2001) 257-264. [18] A.H. Nayfeh, Problems in Perturbation, John Wiley, New York, (1985). [19] E.J. Parkes, B.R. Duy, An automated tanh-function method for nding solitary wave solutions to non-linear evolution equations, Comput. Phys. Commun. 98 (1996), 288-300.

[20] W. Hereman, P.P. Banerjee, A. Korpel, G. Assanto, A. van Immerzeele, A. Meer- poel, Exact solitary wave solutions of nonlinear evolution and wave equations using a direct algebraic method, J. Phys. A: Math. Gen. 19 (1986) 607-628.