Analysis of an element-free Galerkin method for the nonlinear Schrödinger equation

DOI10.1016/j.matcom.2022.06.031OpenAlexW4285012669WikidataQ113869123 ScholiaQ113869123MaRDI QIDQ2079350

Shuling Li, Xiao-Lin Li

Publication date: 29 September 2022

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matcom.2022.06.031

zbMATH Keywords

element-free Galerkin methoderror estimatemeshless methodstime-dependent Schrödinger equationerror splitting technique

Mathematics Subject Classification ID

Mechanics of deformable solids (74-XX) Numerical analysis (65-XX)

Cites Work

• Unnamed Item
• An element-free based solution for nonlinear Schrödinger equations using the ICVMLS-Ritz method
• Fourth-order compact and energy conservative difference schemes for the nonlinear Schrödinger equation in two dimensions
• The meshless local Petrov-Galerkin (MLPG) method for the generalized two-dimensional nonlinear Schrödinger equation
• On the stability of the moving least squares approximation and the element-free Galerkin method
• An energy-preserving Crank-Nicolson Galerkin spectral element method for the two dimensional nonlinear Schrödinger equation
• Error estimates for the moving least-square approximation and the element-free Galerkin method in \(n\)-dimensional spaces
• Finite-difference solutions of a non-linear Schrödinger equation
• Difference schemes for solving the generalized nonlinear Schrödinger equation
• The nonlinear Schrödinger equation. Self-focusing and wave collapse
• An efficient numerical technique for solution of two-dimensional cubic nonlinear Schrödinger equation with error analysis
• Unconditional optimal error estimates for BDF2-FEM for a nonlinear Schrödinger equation
• A numerical scheme based on radial basis function finite difference (RBF-FD) technique for solving the high-dimensional nonlinear Schrödinger equations using an explicit time discretization: Runge-Kutta method
• A linearized element-free Galerkin method for the complex Ginzburg-Landau equation
• A meshfree approach for analysis and computational modeling of non-linear Schrödinger equation
• Analysis of an augmented moving least squares approximation and the associated localized method of fundamental solutions
• The improved complex variable element-free Galerkin method for two-dimensional Schrödinger equation
• A meshless symplectic method for two-dimensional nonlinear Schrödinger equations based on radial basis function approximation
• Element‐free Galerkin methods
• Superconvergence analysis of a new linearized MFEM for nonlinear Schrödinger equation
• A Galerkin Splitting Symplectic Method for the Two Dimensional Nonlinear Schrödinger Equation
• Numerical Simulation of Non-Linear Schrodinger Equations in Arbitrary Domain by the Localized Method of Approximate Particular Solution
• A meshless method and stability analysis for the nonlinear Schrödinger equation