An efficient numerical method based on Variational iteration method for solving the Kuramoto-Sivashinsky equations
Résumé
In this paper we consider variational iteration method to investigate solution of Kuramoto-Sivashinsky equations. Comparison of the results of this method obtained just in 2-iterations with RBF based mesh -free method and local continuous Galerkin methods, shows the efficiency of this method. Numerical experiments are included to show the efficiency of this method.Téléchargements
Références
G. Akrivis, Y-Sokratis Smyrlis, Implicit-explicit BDF methods for the Kuramoto-Sivashinsky equation, Appl. Numer. Math 51 (2004) 151- 169.
G. h. E. Draganescu, V.Capalnasan, Nonlinear relaxation phenomena in polycrystalline solids, Int J Nonlinear Sci Numer Simul 4(3) (2003), 219-226.
J. H. He, X. H. Wu, Construction of solitary solution and compacton-like solution by variational iteration method, Chaos, Solitons and Fractals 29 (1) (2006), 108-113.
J. H. He, Y. Q. Wan, Q. Guo, An iteration formulation for normalized diode characteristics, Int. J. Circuit Theory Appl 32(6) (2004), 629-632.
J. H. He, Variational iteration method a kind of non-linear analytical technique: Some examples, International Journal of Non-Linear Mechanics 34 (4) (1999), 699-708.
J. H. He, Approximate analytical solution for seepage flow with fractional derivatives in porous media, Computer Methods in Applied Mechanics and Engineering 167 (1-2) (1998), 57-68.
J. H. He, Approximate solution of nonlinear differential equations with convolution product nonlinearities, Computer Methods in Applied Mechanics and Engineering 167 (1-2) (1998), 69-73.
J. H. He, Variational iteration method for autonomous ordinary differential systems, Applied Mathematics and Computation 118 (23) (2000), 115-123.
A. P. Hooper, R. Grimshaw, Travelling wave solutions of the KuramotoSivashinsky equation, Wave Motion 10 (1988), 405-420.
A. P. Hooper, R. Grimshaw, Nonlinear instability at the interface between two viscous fluids, Phys. Fluids 28 (1985), 37-45.
Y. Kuramoto, T. Tsuzuki, Persistent propagation of concentration waves in dissipative media far from thermal equilibrium, Stochastics Theor. Phys. 55 (1976) 356.
H. Lai, C. Ma, Lattice Boltzmann method for the generalized Kuramoto-Sivashinsky equation, Physica A 388 (2009), 1405-1412.
M. A. Lopez-Marcos, Numerical analysis of pseudospectral method for the Kuramoto-Sivashinsky equation, IMA J. Numer. Anal. 14 (1994), 223-242.
A. V. Manickam, K. M. Moudgalya, A. K. Pani, Second-order splitting combined with orthogonal cubic spline collocation method for the Kuramoto Sivashinsky equation, Comput. Math. Appl. 35 (1998), 5-25.
D. Michelson, Steady solutions of the Kuramoto-Sivashinsky equation, Physica D 19 (1986), 89-111.
S. Momani, S. Abuasad, Z. Odibat, Variational iteration method for solving nonlinear boundary value problems, Journal of Applied Mathematics and Computation 2006, 183, 1351-1358.
M. Rafei, H. Daniali, D. D. Ganji, Variational iteration method for solving the epidemic model and the prey and predator problem, Journal of Applied Mathematics and Computation 2007, 186, 1701-1709.
G. I. Sivashinsky, Instabilities, pattern-formation and turbulance in flames, Rev, Fluid Mech.15 (1983), 179-199.
M. Uddin, S. Haq, Siraj-ul-Islam, A mesh-free numerical method for solution of the family of Kuramoto-Sivashinsky equations, Applied Mathematics and Computation 212 (2009), 458-469.
Y. Xu, C. W Shu, Local discontinuous Galerkin methods for the Kuramoto-Sivashinsky equations and the Ito-type coupled KdV equations, Comput. Methods Appl. Mech. Eng. 195 (2006), 3430-3447.
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