Long-time simulations of nonlinear Schrödinger-type equations using step size exceeding threshold of numerical instability

DOI10.1007/s10915-016-0346-yzbMath1371.65081OpenAlexW2562976995MaRDI QIDQ2399151

T. I. Lakoba

Publication date: 22 August 2017

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-016-0346-y

zbMATH Keywords

numerical examplesnumerical instabilitynonlinear wave equationsnonlinear Schrödinger-type equationsFourier split-step methodstatistics of nonlinear waves

Mathematics Subject Classification ID

Second-order nonlinear hyperbolic equations (35L70) 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)

Related Items (3)

Comparison of split-step and Hamiltonian integration methods for simulation of the nonlinear Schrödinger type equations ⋮ Stability analysis of the numerical method of characteristics applied to a class of energy-preserving hyperbolic systems. I: Periodic boundary conditions ⋮ Numerical study of solitary wave stability in cubic nonlinear Dirac equations in 1D

Cites Work

• Unnamed Item
• Effect of noise on extreme events probability in a one-dimensional nonlinear Schrödinger equation
• Computational methods for the dynamics of the nonlinear Schrödinger/Gross-Pitaevskii equations
• Krylov implicit integration factor WENO methods for semilinear and fully nonlinear advection-diffusion-reaction equations
• Influence of the condensate and inverse cascade on the direct cascade in wave turbulence
• Numerical simulation of a solitonic gas in KdV and KdV-BBM equations
• An accurate polynomial approximation of exponential integrators
• Operator splitting implicit integration factor methods for stiff reaction-diffusion-advection systems
• Exponential time differencing for stiff systems
• Dynamics of the center of mass in rotating Bose-Einstein condensates
• Focusing: A mechanism for instability of nonlinear finite difference equations
• Numerical simulation of nonlinear Schrödinger systems: A new conservative scheme
• Simulation of coherent structures in nonlinear Schrödinger-type equations
• Krylov integration factor method on sparse grids for high spatial dimension convection-diffusion equations
• Semi-analytical time differencing methods for stiff problems
• Fast explicit integration factor methods for semilinear parabolic equations
• Fast high-order compact exponential time differencing Runge-Kutta methods for second-order semilinear parabolic equations
• Instability of the finite-difference split-step method applied to the nonlinear Schrödinger equation. I. standing soliton
• Instability analysis of the split-step Fourier method on the background of a soliton of the nonlinear Schrödinger equation
• Fourier Methods with Extended Stability Intervals for the Korteweg–de Vries Equation
• Split-Step Methods for the Solution of the Nonlinear Schrödinger Equation
• A numerical and theoretical study of certain nonlinear wave phenomena
• Geometric numerical integration illustrated by the Störmer–Verlet method
• A PseudoSpectral Procedure for the Solution of Nonlinear Wave Equations with Examples from Free-Surface Flows
• Plane wave stability of some conservative schemes for the cubic Schrödinger equation
• Generalized Runge-Kutta Processes for Stable Systems with Large Lipschitz Constants
• An exponential method of numerical integration of ordinary differential equations
• Geometric integrators for the nonlinear Schrödinger equation

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