Linear high-order energy-preserving schemes for the nonlinear Schrödinger equation with wave operator using the scalar auxiliary variable approach

DOI10.1007/s10915-021-01533-9zbMath1480.35358OpenAlexW3171386003MaRDI QIDQ2049096

Yuezheng Gong, Lu-Ming Zhang, Xin Li

Publication date: 24 August 2021

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

Full work available at URL: https://doi.org/10.1007/s10915-021-01533-9

zbMATH Keywords

energy-preservingsymplectic Runge-Kutta methodlinear high-order schemesprediction-correctionnonlinear Schrödinger equation with wave operatorscalar auxiliary variable

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) NLS equations (nonlinear Schrödinger equations) (35Q55) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (9)

High-order conservative energy quadratization schemes for the Klein-Gordon-Schrödinger equation ⋮ Arbitrary high-order linear structure-preserving schemes for the regularized long-wave equation ⋮ High-order Lagrange multiplier method for the coupled Klein-Gordon-Schrödinger system ⋮ On convergence of a novel linear conservative scheme for the two-dimensional fractional nonlinear Schrödinger equation with wave operator ⋮ Mass- and energy-conserving Gauss collocation methods for the nonlinear Schrödinger equation with a wave operator ⋮ Two energy-preserving Fourier pseudo-spectral methods and error estimate for the Klein-Gordon-Dirac system ⋮ Mass-, and energy preserving schemes with arbitrarily high order for the Klein-Gordon-Schrödinger equations ⋮ High-order structure-preserving Du Fort-Frankel schemes and their analyses for the nonlinear Schrödinger equation with wave operator ⋮ Unconditional optimal error estimates and superconvergence analysis of energy-preserving FEM for general nonlinear Schrödinger equation with wave operator

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