Plane wave stability of some conservative schemes for the cubic Schrödinger equation

DOI10.1051/m2an/2009022zbMath1167.65449arXiv1011.1062OpenAlexW2148492670MaRDI QIDQ5192616

Brynjulf Owren, Morten Dahlby

Publication date: 6 August 2009

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1011.1062

zbMATH Keywords

stabilityfinite difference methodnonlinear Schrödinger equationenergy conservationlinearly implicit methods

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99)

Related Items (8)

Error Estimation of the Relaxation Finite Difference Scheme for the Nonlinear Schrödinger Equation ⋮ Adaptive splitting methods for nonlinear Schrödinger equations in the semiclassical regime ⋮ Numerical study of fourth-order linearized compact schemes for generalized NLS equations ⋮ Long-time simulations of nonlinear Schrödinger-type equations using step size exceeding threshold of numerical instability ⋮ Surprising computations ⋮ Numerical study of blow-up to the purely elliptic generalized Davey-Stewartson system ⋮ Metastable energy strata in numerical discretizations of weakly nonlinear wave equations ⋮ PLANE WAVE STABILITY OF THE SPLIT-STEP FOURIER METHOD FOR THE NONLINEAR SCHRÖDINGER EQUATION

Cites Work

• Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical, nonlinear Schrödinger equation
• Symmetric exponential integrators with an application to the cubic Schrödinger equation
• Numerical simulation of nonlinear Schrödinger systems: A new conservative scheme
• Split-Step Methods for the Solution of the Nonlinear Schrödinger Equation
• A Nonlinear Difference Scheme and Inverse Scattering
• The numerical integration of relative equilibrium solutions. The nonlinear Schrodinger equation
• A Relaxation Scheme for the Nonlinear Schrödinger Equation
• Geometric Numerical Integration
• Dissipative or conservative finite-difference schemes for complex-valued nonlinear partial differential equations
• Geometric integrators for the nonlinear Schrödinger equation

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