Numerical solution of seven-order Sawada-Kotara equations by homotopy perturbation method
Subject Areas : Applied MathematicsM. 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.
Keywords:
Abstract :
In this paper, an application of homotopy perturbation method is appliedto nding the solutions of the seven-order Sawada-Kotera (sSK) and a Lax'sseven-order KdV (LsKdV) equations. Then obtain the exact solitary-wave so-lutions and numerical solutions of the sSK and LsKdV equations for the initialconditions. The numerical solutions are compared with the known analyticalsolutions. Their remarkable accuracy are nally demonstrated for the bothseven-order equations.
[1] M. Ghasemi, M. Tavassoli Kajani, Application of He's homotopy perturbation
method for linear and nonlinear heat equations, Math. Scienti c 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. Scienti c J. 1 (5) (2009)
47-55.
[3] M. Ghasemi, M. Tavassoli Kajani, A. Davari, Numerical solution of two-
dimensional nonlinear di erential 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-di erential equations, Appl. Math.
Comput. 188 (2007) 538-548.
[6] M. Ghasemi, M. Tavassoli Kajani, Application of He's homotopy perturbation
method to solve a di usion-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. Du y, 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.
