The existence of the global solution of the semi-linear Schrödinger equation with numerical computation on the Dirichlet boundary
type: Item
instance of: scholarly article
title: The existence of the global solution of the semi-linear Schrödinger equation with numerical computation on the Dirichlet boundary
DOI: 10.11948/20240161
author: Pius W. M. Chin
published in: Journal of Applied Analysis and Computation
publication date: 2024-12-20T00:00:00Z
Mathematics Subject Classification ID: 35J47
Mathematics Subject Classification ID: 35J70
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 65N30
zbMATH DE Number: 7960325
zbMATH Keywords: Schrödinger equation
zbMATH Keywords: semi-linear equation
zbMATH Keywords: nonstandard finite difference method
zbMATH Keywords: Galerkin method
zbMATH Keywords: optimal rate of convergence
MaRDI profile type: Publication
cites work: On the numerical solution of Fisher's equation with coefficient of diffusion term much smaller than coefficient of reaction term
cites work: Contributions to the mathematics of the nonstandard finite difference method and applications
cites work: Nonstandard finite difference method by nonlocal approximation
cites work: Comparison of modified ADM and classical finite difference method for some third-order and fifth-order KdV equations
cites work: Higher order exponential time differencing scheme for system of coupled nonlinear Schrödinger equations
cites work: Nonlinear Schrödinger evolution equations
cites work: Local energy-preserving and momentum-preserving algorithms for coupled nonlinear Schrödinger system
cites work: Solution of the forced nonlinear schrödinger (nls) equation using pde techniques
cites work: Multi-symplectic splitting method for the coupled nonlinear Schrödinger equation
cites work: The analysis of an efficient numerical scheme for the Allen-Cahn equations using the Galerkin method
cites work: The analysis of the solution of the <scp>Burgers–Huxley</scp> equation using the Galerkin method
cites work: The effect on the solution of the Fitzhugh-Nagumo equation by the external parameter \(\alpha \) using the Galerkin method
cites work: Q4162607
cites work: Q4399897
cites work: Numerical and mathematical analysis of a nonlinear Schrödinger problem with moving ends
cites work: Conservative compact difference schemes for the coupled nonlinear schrödinger system
cites work: Multiple solutions for nonhomogeneous quasilinear Schrödinger-Poisson system
cites work: A linearly implicit conservative scheme for the coupled nonlinear Schrödinger equation
cites work: Compact and efficient conservative schemes for coupled nonlinear <scp>S</scp>chrödinger equations
cites work: The boundary value problems of mathematical physics. Transl. from the Russian by Jack Lohwater
cites work: Nontrivial generalized solution of Schrödinger-Poisson system in \(\mathbb{R}^3\) with zero mass and periodic potential
cites work: Decay properties and asymptotic behavior of positive solutions for the nonlinear fractional Schrödinger-Poisson system
cites work: Q5634306
cites work: High-order compact splitting multisymplectic method for the coupled nonlinear Schrödinger equations
cites work: Q4309510
cites work: On the use of nonstandard finite difference methods†
cites work: Q4340096
cites work: Long time stability and convergence for fully discrete nonlinear galerkin methods
cites work: Strong coupling of Schrödinger equations: conservative scheme approach
cites work: A non-linear instability theory for a wave system in plane Poiseuille flow
cites work: The nonlinear Schrödinger equation. Self-focusing and wave collapse
cites work: Q3684480
cites work: Infinite-dimensional dynamical systems in mechanics and physics.
cites work: On smooth solutions to the initial-boundary value problem for the nonlinear schrödinger equation in two space dimensions
cites work: On global solutions to the initial–boundary value problem for the nonlinear Schrödinger equations in exterior domains
cites work: Global solutions of the nonlinear schrödinger equation in exterior domains
cites work: Maximum norm error bound of a linearized difference scheme for a coupled nonlinear Schrödinger equations
cites work: Exact solutions for the fourth order nonlinear Schrödinger equations with cubic and power law nonlinearities
cites work: A Priori $L_2 $ Error Estimates for Galerkin Approximations to Parabolic Partial Differential Equations
description: scientific article; zbMATH DE number 7960325