Strang splitting methods for a quasilinear Schrödinger equation: convergence, instability, and dynamics
نویسندگان
چکیده
منابع مشابه
Strang Splitting Methods for a Quasilinear Schrödinger Equation - Convergence, Instability and Dynamics
We study the Strang splitting scheme for quasilinear Schrödinger equations. We establish the convergence of the scheme for solutions with small initial data. We analyze the linear instability of the numerical scheme, which explains the numerical blow-up of large data solutions and connects to analytical breakdown of regularity of solutions to quasilinear Schrödinger equations. Numerical tests a...
متن کاملStrang Splitting Methods Applied to a Quasilinear Schrödinger Equation - Convergence and Dynamics
We study numerically a class of quasilinear Schrödinger equations using the Strang splitting method. For these particular models, we can prove convergence of our approximation by adapting the work of Lubich [30] for a Lie theoretic approach to the continuous time approximation and Sobolev-based well-posedness results of the second author with J. Metcalfe and D. Tataru in order to model small in...
متن کاملStrang Splitting for the Time-Dependent Schrödinger Equation on Sparse Grids
The time-dependent Schrödinger equation is discretized in space by a sparse grid pseudo-spectral method. The Strang splitting for the resulting evolutionary problem features first or second order convergence in time, depending on the smoothness of the potential and of the initial data. In contrast to the full grid case, where the frequency domain is the working place, the proof of the sufficien...
متن کاملConvergence of a semiclassical wavepacket based time-splitting for the Schrödinger equation
We propose a new algorithm for solving the semiclassical time– dependent Schrödinger equation. The algorithm is based on semiclassical wavepackets. The focus of the analysis is only on the time discretization: convergence is proved to be quadratic in the time step and linear in the semiclassical parameter ε.
متن کاملConvergence Properties of Hermitian and Skew Hermitian Splitting Methods
In this paper we consider the solutions of linear systems of saddle point problems. By using the spectrum of a quadratic matrix polynomial, we study the eigenvalues of the iterative matrix of the Hermitian and skew Hermitian splitting method.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications in Mathematical Sciences
سال: 2015
ISSN: 1539-6746,1945-0796
DOI: 10.4310/cms.2015.v13.n5.a1