FULLY DISCRETE SCHEMES FOR THE SCHRÖDINGER EQUATION: DISPERSIVE PROPERTIES

DOI10.1142/S0218202507002029zbMath1135.65033MaRDI QIDQ5297206

Liviu I. Ignat

Publication date: 18 July 2007

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

zbMATH Keywords

error estimatesdiscrete Fourier transformfinite differencesbackward Euler methodCrank-Nicolson methodsFourier multipliers, Strichartz estimates, Schrödinger equation

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) PDEs in connection with quantum mechanics (35Q40) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items (11)

An inhomogeneous space-time patching model based on a nonlocal and nonlinear Schrödinger equation ⋮ Two-point correlation function and its applications to the Schrödinger-Lohe type models ⋮ Convergence analysis of the splitting method to the nonlinear heat equation ⋮ Uniform Strichartz estimates on the lattice ⋮ A splitting method for the nonlinear Schrödinger equation ⋮ Strong Convergence for Discrete Nonlinear Schrödinger equations in the Continuum Limit ⋮ Convergence rates for dispersive approximation schemes to nonlinear Schrödinger equations ⋮ Finite difference scheme for two-dimensional periodic nonlinear Schrödinger equations ⋮ On the splitting method for the nonlinear Schrödinger equation with initial data in \(H^1\) ⋮ On the continuum limit for the discrete nonlinear Schrödinger equation on a large finite cubic lattice ⋮ DISPERSIVE SCHEMES FOR THE CRITICAL KORTEWEG–DE VRIES EQUATION

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Small solutions to nonlinear Schrödinger equations
• The Cauchy problem for the nonlinear Schrödinger equation in \(H^ 1\)
• The global Cauchy problem for the nonlinear Schrödinger equation revisited
• Existence of solutions for Schrödinger evolution equations
• Ensuring well-posedness by analogy; Stokes problem and boundary control for the wave equation
• Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations
• The nonlinear Schrödinger equation. Self-focusing and wave collapse
• Discrete analogues in harmonic analysis: spherical averages
• Dispersive properties of a viscous numerical scheme for the Schrödinger equation
• A two-grid approximation scheme for nonlinear Schrödinger equations: dispersive properties and convergence
• Fonctions entières et intégrales de Fourier multiples. II
• A First Course in the Numerical Analysis of Differential Equations
• Endpoint Strichartz estimates
• Theoretical Numerical Analysis
• Asymptotic behaviour of small solutions for the discrete nonlinear Schrödinger and Klein–Gordon equations
• Stability and Convergence Rates in $L^p$ for Certain Difference Schemes.

This page was built for publication: FULLY DISCRETE SCHEMES FOR THE SCHRÖDINGER EQUATION: DISPERSIVE PROPERTIES