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.
Highlights
Kuramoto-Sivashinsky equationsThere are two standard forms for the kuramoto-Sivashinsky equation
Initial condition for this equation is L-periodic initial condition with L > 0
By using an initial function u0, the approximations un+1, n ≥ 0 of the solution u(x, t) can be obtained via the calculated Lagrange multiplier and the exact solution can be obtained by u(x, t)
Summary
There are two standard forms for the kuramoto-Sivashinsky equation. Initial condition for this equation is L-periodic initial condition with L > 0. Another kind of Kuramoto-Sivashinsky equation is as follows: ut + uux − uxx + uxxxx = 0. The initial condition for this equation is: L u(x, 0)dx = 0. The Kuramoto-Sivashinsky equation is similar to Burgers equation, because of presence of second and fourth order derivatives, this equation has more complicated behavior. The sign of second derivative term is such that it operate as an energy source. The nonlinear part of the equation uux transfers energy between low to high level wave numbers
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