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 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...

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.

We analyse the nonlinear Kuramoto–Sivashinsky equation to develop accurate discretisations modeling its dynamics on coarse grids. The analysis is based upon centre manifold theory so we are assured that the discretisation accurately models the dynamics and may be constructed systematically. The theory is applied after dividing the physical domain into small elements by introducing isolating int...

In this paper, we consider nonlinear multidimensional Cahn–Hilliard and Kuramoto–Sivashinsky equations that have many important applications in physics chemistry, a certain natural generalization of these two to which refer as the generalized Cahn–Hilliard–Kuramoto–Sivashinsky equation. For an arbitrary number spatial independent variables, present complete list cases when latter equation admit...

On the example of a nite dimensional approximation of the Kuramoto-Sivashinsky equation we show how topological methods may be successfully used in computer assisted proofs of the existence of heteroclinic connections in ordinary diierential equations.