Error Analysis of a First-Order IMEX Scheme for the Logarithmic Schrödinger Equation
DOI10.1137/22m1503543arXiv2306.15901OpenAlexW4390805409MaRDI QIDQ6184515
Xiaolong Zhang, Li-Lian Wang, JingYe Yan
Publication date: 25 January 2024
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2306.15901
logarithmic Schrödinger equationnondifferentiabilitylocally Hölder continuitynonlinear Grönwall's inequality
Smoothness and regularity of solutions to PDEs (35B65) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Error bounds for boundary value problems involving PDEs (65N15) NLS equations (nonlinear Schrödinger equations) (35Q55) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Direct numerical methods for linear systems and matrix inversion (65F05) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22) Time-dependent Schrödinger equations and Dirac equations (35Q41)
Cites Work
- Unnamed Item
- A new error analysis of Crank-Nicolson Galerkin FEMs for a generalized nonlinear Schrödinger equation
- Logarithmic nonlinearity in theories of quantum gravity: origin of time and observational consequences
- On fully discrete Galerkin methods of second-order temporal accuracy for the nonlinear Schrödinger equation
- Universal dynamics for the defocusing logarithmic Schrödinger equation
- Superexponential growth or decay in the heat equation with a logarithmic nonlinearity
- On the convergence of the Crank-Nicolson method for the logarithmic Schrödinger equation
- Bound states for logarithmic Schrödinger equations with potentials unbounded below
- Regularized numerical methods for the logarithmic Schrödinger equation
- Numerical solution of the regularized logarithmic Schrödinger equation on unbounded domains
- Numerical study of the logarithmic Schrödinger equation with repulsive harmonic potential
- Pointwise Best Approximation Results for Galerkin Finite Element Solutions of Parabolic Problems
- Unconditional Convergence and Optimal Error Estimates of a Galerkin-Mixed FEM for Incompressible Miscible Flow in Porous Media
- Error analysis of linearized semi-implicit Galerkin finite element methods for nonlinear parabolic equations
- Équations d'évolution avec non linéarité logarithmique
- Gaussons: Solitons of the Logarithmic Schrödinger Equation
- Error Estimates of a Regularized Finite Difference Method for the Logarithmic Schrödinger Equation
- Dynamics of the Schrödinger–Langevin equation
- Error estimates of local energy regularization for the logarithmic Schrödinger equation
- Logarithmic Bose–Einstein condensates with harmonic potential
- The Mathematical Theory of Finite Element Methods
- Galerkin Finite Element Methods for Parabolic Problems
- Logarithmic Schrödinger equation with quadratic potential*
- Nonuniqueness and nonlinear instability of Gaussons under repulsive harmonic potential
- An efficient spectral trust-region deflation method for multiple solutions
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