Maximum norm error estimates of fourth-order compact difference scheme for the nonlinear Schrödinger equation involving a quintic term
DOI10.1186/s13660-018-1775-yzbMath1498.65136OpenAlexW2883710638WikidataQ91103327 ScholiaQ91103327MaRDI QIDQ824681
Publication date: 15 December 2021
Published in: Journal of Inequalities and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1186/s13660-018-1775-y
convergenceunconditional stabilitySchrödinger equationconservationcompact finite difference schememax normquintic term
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) NLS equations (nonlinear Schrödinger equations) (35Q55) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A compact split-step finite difference method for solving the nonlinear Schrödinger equations with constant and variable coefficients
- Compact finite difference schemes with high accuracy for one-dimensional nonlinear Schrödinger equation
- Efficient finite difference solutions to the time-dependent Schrödinger equation
- On fully discrete Galerkin methods of second-order temporal accuracy for the nonlinear Schrödinger equation
- Difference schemes for solving the generalized nonlinear Schrödinger equation
- The nonlinear Schrödinger equation. Self-focusing and wave collapse
- Third order implicit-explicit Runge-Kutta local discontinuous Galerkin methods with suitable boundary treatment for convection-diffusion problems with Dirichlet boundary conditions
- Numerical simulation of nonlinear Schrödinger systems: A new conservative scheme
- A compact finite difference scheme for the nonlinear Schrödinger equation with wave operator
- The stability and convergence of a difference scheme for the Schrödinger equation on an infinite domain by using artificial boundary conditions
- Optimal Point-Wise Error Estimate of a Compact Finite Difference Scheme for the Coupled Nonlinear Schrödinger Equations
- Error Estimate of Fourth-Order Compact Scheme for Linear Schrödinger Equations
- Maximum norm error bounds of ADI and compact ADI methods for solving parabolic equations
- An Unconditionally Stable Three-Level Explicit Difference Scheme for the Schrödinger Equation with a Variable Coefficient
- Some pointwise estimates for the finite element solution of a radial nonlinear Schrödinger equation on a class of nonuniform grids
- Discrete-time Orthogonal Spline Collocation Methods for Schrödinger Equations in Two Space Variables
- An Explicit Unconditionally Stable Numerical Method for Solving Damped Nonlinear Schrödinger Equations with a Focusing Nonlinearity
- On Optimal Order Error Estimates for the Nonlinear Schrödinger Equation
- Dufort–Frankel-Type Methods for Linear and Nonlinear Schrödinger Equations
- 一维非线性Schrödinger 方程的两个无条件收敛的守恒紧致差分格式
- A linearized, decoupled, and energy‐preserving compact finite difference scheme for the coupled nonlinear Schrödinger equations
- Analysis of a Fourth‐Order Scheme for a Three‐Dimensional Convection‐Diffusion Model Problem
- Convergence of Fourth Order Compact Difference Schemes for Three‐Dimensional Convection‐Diffusion Equations
This page was built for publication: Maximum norm error estimates of fourth-order compact difference scheme for the nonlinear Schrödinger equation involving a quintic term
