Optimal point-wise error estimate of a compact difference scheme for the coupled Gross-Pitaevskii equations in one dimension
From MaRDI portal
Publication:461210
DOI10.1007/s10915-013-9757-1zbMath1296.65116OpenAlexW2018534386MaRDI QIDQ461210
Publication date: 10 October 2014
Published in: Journal of Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10915-013-9757-1
conservationcompact finite difference schemecoupled Gross-Pitaevskii equationsconvergence in maximum norm
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)
Related Items
Multisymplectic structure-preserving scheme for the coupled Gross–Pitaevskii equations, An efficient split-step compact finite difference method for the coupled Gross–Pitaevskii equations, Conservative compact difference scheme for the Zakharov–Rubenchik equations, Mean-square numerical approximations to random periodic solutions of stochastic differential equations, Point-wise error estimate of a conservative difference scheme for the fractional Schrödinger equation, Maximum-norm error analysis of a difference scheme for the space fractional CNLS, Shadowing orbits of a class of random differential equations, Numerical study of fourth-order linearized compact schemes for generalized NLS equations, Conservative compact finite difference scheme for the coupled <scp>S</scp>chrödinger–<scp>B</scp>oussinesq equation, A new three-level fourth-order compact finite difference scheme for the extended Fisher-Kolmogorov equation, A new compact finite difference scheme for solving the complex Ginzburg-Landau equation, Unconditional and optimal \(H^{1}\) error estimate of a Crank-Nicolson finite difference scheme for the Gross-Pitaevskii equation with an angular momentum rotation term, A mass‐ and energy‐preserving numerical scheme for solving coupled Gross–Pitaevskii equations in high dimensions, Optimal point-wise error estimates of two conservative finite difference schemes for the coupled Gross-Pitaevskii equations with angular momentum rotation terms, An efficient and conservative compact finite difference scheme for the coupled Gross-Pitaevskii equations describing spin-1 Bose-Einstein condensate, A new high-accuracy difference method for nonhomogeneous time-fractional Schrödinger equation, Conservative Three-Level Linearized Finite Difference Schemes for the Fisher Equation and Its Maximum Error Estimates, A difference scheme and its error analysis for a Poisson equation with nonlocal boundary conditions, Dynamical analysis in explicit continuous iteration algorithm and its applications, Numerical study of random periodic Lipschitz shadowing of stochastic differential equations, Unconditional \(L^{\infty}\) convergence of a conservative compact finite difference scheme for the N-coupled Schrödinger-Boussinesq equations, A conservative compact difference scheme for the Zakharov equations in one space dimension, A conservative compact finite difference scheme for the coupled Schrödinger-KdV equations, A conservative sine pseudo-spectral-difference method for multi-dimensional coupled Gross-Pitaevskii equations, An Energy-Preserving Scheme for the Coupled Gross-Pitaevskii Equations, Study on the dynamics of a nonlinear dispersion model in both 1D and 2D based on the fourth-order compact conservative difference scheme, Numerical study on stochastic diabetes mellitus model with additive noise, An efficient implementation of fourth-order compact finite difference scheme for Poisson equation with Dirichlet boundary conditions, A compact difference scheme for a two dimensional nonlinear fractional Klein-Gordon equation in polar coordinates, Optimal error estimate of a compact scheme for nonlinear Schrödinger equation, Numerical analysis for fourth-order compact conservative difference scheme to solve the 3D Rosenau-RLW equation, Numerical approximation of solution for the coupled nonlinear Schrödinger equations, Unconditional convergence of linearized implicit finite difference method for the 2D/3D Gross-Pitaevskii equation with angular momentum rotation, A compact difference scheme for a two dimensional fractional Klein-Gordon equation with Neumann boundary conditions, Numerical study of a conservative weighted compact difference scheme for the symmetric regularized long wave equations, Operator-compensation methods with mass and energy conservation for solving the Gross-Pitaevskii equation, A high‐order compact scheme for the nonlinear fractional <scp>K</scp>lein–<scp>G</scp>ordon equation, Efficiently energy-dissipation-preserving ADI methods for solving two-dimensional nonlinear Allen-Cahn equation, A linearized, decoupled, and energy‐preserving compact finite difference scheme for the coupled nonlinear Schrödinger equations, Numerical analysis of a conservative linear compact difference scheme for the coupled Schrödinger–Boussinesq equations, Optimal error estimates of explicit finite difference schemes for the coupled Gross–Pitaevskii equations
Cites Work
- Fourth-order compact and energy conservative difference schemes for the nonlinear Schrödinger equation in two dimensions
- A three level linearized compact difference scheme for the Cahn-Hilliard equation
- Fourth-order alternating direction implicit compact finite difference schemes for two-dimensional Schrödinger equations
- Compact finite difference schemes with high accuracy for one-dimensional nonlinear Schrödinger equation
- Numerical simulation of nonlinear Schrödinger systems: A new conservative scheme
- Mathematical theory and numerical methods for Bose-Einstein condensation
- Convergence of an eighth-order compact difference scheme for the nonlinear Schrödinger equation
- Dynamics of rotating two-component Bose-Einstein condensates and its efficient computation
- Uniform Error Estimates of Finite Difference Methods for the Nonlinear Schrödinger Equation with Wave Operator
- Compact Alternating Direction Implicit Scheme for the Two-Dimensional Fractional Diffusion-Wave Equation
- Error Estimate of Fourth-Order Compact Scheme for Linear Schrödinger Equations
- Convergence of compact ADI method for solving linear Schrödinger equations
- Maximum norm error bounds of ADI and compact ADI methods for solving parabolic equations
- Ground States and Dynamics of Multicomponent Bose--Einstein Condensates
- Finite Difference Calculus Invariant Structure of a Class of Algorithms for the Nonlinear Klein–Gordon Equation
- Optimal error estimates of finite difference methods for the Gross-Pitaevskii equation with angular momentum rotation
- The number of cubic partitions modulo powers of 5
- VORTICES IN MULTICOMPONENT BOSE–EINSTEIN CONDENSATES
- Ground States of Two-component Bose-Einstein Condensates with an Internal Atomic Josephson Junction
- 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
- Unnamed Item
- Unnamed Item
- Unnamed Item