we show how daubechies wavelets are used to solve kuramoto-sivashinsky type equations with periodic boundary condition‎. ‎wavelet bases are used for numerical solution of the kuramoto-sivashinsky type equations by galerkin method‎. ‎the numerical results in comparison with the exact solution prove the efficiency and accuracy of our method‎.

We show how Daubechies wavelets are used to solve Kuramoto-Sivashinsky type equations with periodic boundary condition‎. ‎Wavelet bases are used for numerical solution of the Kuramoto-Sivashinsky type equations by Galerkin method‎. ‎The numerical results in comparison with the exact solution prove the efficiency and accuracy of our method‎.    

Kuramoto-Sivashinsky equation was introduced by Kuramoto [1976] in one-spatial dimension, for the study of phase turbulance in the BelousovZhabotinsky reaction. Sivashinsky derived it independently in the context of small thermal diffusive instabilities for laminar flame fronts. It and related equations have also been used to model directional solidification and , in multiple spatial dimensions...

A non linear Itô equation in a Hilbert space is studied by means of Girsanov theorem. We consider a non linearity of polynomial growth in suitable norms, including that of quadratic type which appears in the Kuramoto–Sivashinsky equation and in the Navier– Stokes equation. We prove that Girsanov theorem holds for the 1-dimensional stochastic Kuramoto–Sivashinsky equation and for a modification ...

We analyze the discretization of the periodic initial value problem for Kuramoto–Sivashinsky type equations with Burgers nonlinearity by implicit– explicit backward difference formula (BDF) methods, establish stability and derive optimal order error estimates. We also study discretization in space by spectral methods.

in this paper, the solution of the evolutionaryfourth-order in space, sivashinsky equation is obtained by meansof homotopy perturbation method (textbf{hpm}). the results revealthat the method is very effective, convenient  and quite accurateto systems of nonlinear partial differential equations.

We continue to study a simple integro-differential equation: the Quasi-Steady equation (QS) of flame front dynamics. This second order quasi-linear parabolic equation with a non-local term is dynamically similar to the Kuramoto-Sivashinsky (KS) equation. In [FGS03], where it was introduced, its well-posedness and proximity for finite time intervals to the KS equation in Sobolev spaces of period...

In this paper, the solution of the evolutionaryfourth-order in space, Sivashinsky equation is obtained by meansof homotopy perturbation method (textbf{HPM}). The results revealthat the method is very effective, convenient  and quite accurateto systems of nonlinear partial differential equations.

We derive a priori estimates on the absorbing ball in L2 for the stabilized and destabilized Kuramoto-Sivashinsky (KS) equations, and for a sixth-order analog, the Nikolaevskiy equation, and in each case obtain bounds whose parameter dependence is demonstrably optimal. This is done by extending a Lyapunov function construction developed by Bronski and Gambill (Nonlinearity 19, 2023–2039 (2006))...