Implicit–explicit Bdf Methods for the Kuramoto–sivashinsky Equation
نویسنده
چکیده
We consider the periodic initial value problem for the Kuramoto–Sivashinsky (KS) equation. We approximate the solution by discretizing in time by implicit–explicit BDF schemes and in space by a pseudo–spectral method. We present the results of various numerical experiments.
منابع مشابه
Backward Difference Formulae for Kuramoto–sivashinsky Type Equations∗
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.
متن کاملLinearly implicit schemes for multi-dimensional Kuramoto–Sivashinsky type equations arising in falling film flows
This study introduces, analyses and implements space-time discretizations of two-dimensional active dissipative partial differential equations such as the Topper–Kawahara equation; this is the two-dimensional extension of the dispersively modified Kuramoto–Sivashinsky equation found in falling film hydrodynamics. The spatially periodic initial value problem is considered as the size of the peri...
متن کاملExact Solutions of the Generalized Kuramoto-Sivashinsky Equation
In this paper we obtain exact solutions of the generalized Kuramoto-Sivashinsky equation, which describes manyphysical processes in motion of turbulence and other unstable process systems. The methods used to determine the exact solutions of the underlying equation are the Lie group analysis and the simplest equation method. The solutions obtained are then plotted.
متن کاملApplication of Daubechies wavelets for solving Kuramoto-Sivashinsky type equations
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.
متن کاملA Fully Nonlinear Equation for the Flame Front in a Quasi-steady Combustion Model
We revisit the Near Equidiffusional Flames (NEF) model introduced by Matkowsky and Sivashinsky in 1979 and consider a simplified, quasisteady version of it. This simplification allows, near the planar front, an explicit derivation of the front equation. The latter is a pseudodifferential fully nonlinear parabolic equation of the fourth-order. First, we study the (orbital) stability of the null ...
متن کامل