Operator splitting for the KdV equation
نویسندگان
چکیده
We provide a new analytical approach to operator splitting for equations of the type ut = Au + B(u) where A is a linear operator and B is quadratic. A particular example is the Korteweg–de Vries (KdV) equation ut−uux +uxxx = 0. We show that the Godunov and Strang splitting methods converge with the expected rates if the initial data are sufficiently regular.
منابع مشابه
Operator Splitting for Kdv
We apply the method of operator splitting on the generalized Korteweg{de Vries (KdV) equation ut +f(u)x+"uxxx = 0, by solving the nonlinear conservation law ut +f(u)x = 0 and the linear dispersive equation ut + "uxxx = 0 sequentially. We prove that if the approximation obtained by operator splitting converges, then the limit function is a weak solution of the generalized KdV equation. Convergen...
متن کاملApplication of the Kudryashov method and the functional variable method for the complex KdV equation
In this present work, the Kudryashov method and the functional variable method are used to construct exact solutions of the complex KdV equation. The Kudryashov method and the functional variable method are powerful methods for obtaining exact solutions of nonlinear evolution equations.
متن کاملOrder reduction and μ-conservation law for the non-isospectral KdV type equation a with variable-coefficients
The goal of this paper is to calculate of order reduction of the KdV typeequation and the non-isospectral KdV type equation using the μ-symmetrymethod. Moreover we obtain μ-conservation law of the non-isospectral KdVtype equation using the variational problem method.
متن کاملOperator Splitting for Well-Posed Active Scalar Equations
We analyze operator splitting methods applied to scalar equations with a nonlinear advection operator, and a linear (local or nonlocal) diffusion operator or a linear dispersion operator. The advection velocity is determined from the scalar unknown itself and hence the equations are so-called active scalar equations. Examples are provided by the surface quasi-geostrophic and aggregation equatio...
متن کاملNumerical method satisfying the first two conservation laws for the Korteweg-de Vries equation
In this paper, we develop a finite-volume scheme for the KdV equation which conserves both the momentum and energy. The main ingredient of the method is a numerical device we developed in recent years that enables us to construct numerical method for a PDE that also simulates its related equations. In the method, numerical approximations to both the momentum and energy are conservatively comput...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Math. Comput.
دوره 80 شماره
صفحات -
تاریخ انتشار 2011