An efficient numerical method based on Variational iteration method for solving the Kuramoto-Sivashinsky equations
Abstract
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.
Downloads
References
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.
Copyright (c) 2020 Boletim da Sociedade Paranaense de Matemática
This work is licensed under a Creative Commons Attribution 4.0 International License.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
