منابع مشابه
Operator splitting for the KdV equation
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.
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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...
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1. I n t r o d u c t i o n . In this paper we shall discuss operator splitting methods to discretize the linear Wigner equation and the coupled Wigner-Poisson system. The Wigner formalism, which represents a phase-space description of quantum mechanics, has in recent years a t t racted considerable at tent ion of solid s tate physicists for including quantum effects in the simulation of ul tra-...
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We present a family of symplectic splitting methods especially tailored to solve numerically the time-dependent Schrodinger equation. When discretized in time, this equation can be recast in the form of a classical Hamiltonian system with a Hamiltonian function corresponding to a generalized high-dimensional separable harmonic oscillator. The structure of the system allows us to build highly ef...
متن کاملA solution of an operator equation related to the KdV equation
For a given nonzero bounded linear operator A on a Banach space X, we show that if A or A∗ has an eigenvalue then, except when the dimension of X is equal to two and the trace of A is zero, there exists a bounded linear operator B on X such that (i) AB + BA is of rank one, and (ii) I + f (A)B is invertible for every function f analytic in a neighborhood of the spectrum of A. This result was mot...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2011
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-2010-02402-0