Dispersive properties of a viscous numerical scheme for the Schrödinger equation

DOI10.1016/j.crma.2005.02.024zbMath1063.35016OpenAlexW2015325106MaRDI QIDQ1773347

Enrique Zuazua, Liviu I. Ignat

Publication date: 28 April 2005

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2005.02.024

zbMATH Keywords

Strichartz inequalityfinite-difference space semi-discretizationsnumerical viscosity term

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) NLS equations (nonlinear Schrödinger equations) (35Q55) Theoretical approximation in context of PDEs (35A35) Schrödinger operator, Schrödinger equation (35J10)

Related Items (17)

CONVERGENCE OF NUMERICAL SCHEMES FOR SHORT WAVE LONG WAVE INTERACTION EQUATIONS ⋮ FULLY DISCRETE SCHEMES FOR THE SCHRÖDINGER EQUATION: DISPERSIVE PROPERTIES ⋮ Continuum limit of 2D fractional nonlinear Schrödinger equation ⋮ Uniform Strichartz estimates on the lattice ⋮ A splitting method for the nonlinear Schrödinger equation ⋮ Dispersive properties for discrete Schrödinger equations ⋮ Strong Convergence for Discrete Nonlinear Schrödinger equations in the Continuum Limit ⋮ Small time uniform controllability of the linear one-dimensional Schrödinger equation with vanishing viscosity ⋮ Uniform Exponential Decay for Viscous Damped Systems* ⋮ Convergence rates for dispersive approximation schemes to nonlinear Schrödinger equations ⋮ Finite difference scheme for two-dimensional periodic nonlinear Schrödinger equations ⋮ Macroscopic behavior of microscopic oscillations in harmonic lattices via Wigner-Husimi transforms ⋮ Uniformly exponentially stable approximations for a class of damped systems ⋮ Convergence of semi-discrete approximations of Benney equations ⋮ A two-grid approximation scheme for nonlinear Schrödinger equations: dispersive properties and convergence ⋮ Uniform controllability for the beam equation with vanishing structural damping ⋮ On the continuum limit for the discrete nonlinear Schrödinger equation on a large finite cubic lattice

Cites Work

• Compact sets in the space \(L^ p(0,T;B)\)
• Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations
• Local Smoothing Properties of Dispersive Equations
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Dispersive properties of a viscous numerical scheme for the Schrödinger equation