Several conservative compact schemes for a class of nonlinear Schrödinger equations with wave operator

DOI10.1186/s13661-018-0956-4zbMath1499.65380OpenAlexW2794501736MaRDI QIDQ2126338

Xiujun Cheng, Fengyan Wu

Publication date: 19 April 2022

Published in: Boundary Value Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13661-018-0956-4

zbMATH Keywords

stabilityconvergencediscrete conservation lawsnonlinear Schrödinger equations with wave operator

Mathematics Subject Classification ID

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) Extrapolation to the limit, deferred corrections (65B05) NLS equations (nonlinear Schrödinger equations) (35Q55) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (11)

Nonlinear conservation laws for the Schrödinger boundary value problems of second order ⋮ A stabilized fully-discrete scheme for phase field crystal equation ⋮ Hamiltonian-preserving schemes for the two-dimensional fractional nonlinear Schrödinger wave equations ⋮ Mass- and energy-conserving Gauss collocation methods for the nonlinear Schrödinger equation with a wave operator ⋮ A high-order structure-preserving difference scheme for generalized fractional Schrödinger equation with wave operator ⋮ Tanh Jacobi spectral collocation method for the numerical simulation of nonlinear Schrödinger equations on unbounded domain ⋮ Uniform Error Bounds of a Conservative Compact Finite Difference Method for the Quantum Zakharov System in the Subsonic Limit Regime ⋮ Convergence of an energy-conserving scheme for nonlinear space fractional Schrödinger equations with wave operator ⋮ Optimal \(l^\infty\) error estimates of the conservative scheme for two-dimensional Schrödinger equations with wave operator ⋮ A linearized compact ADI numerical method for the two-dimensional nonlinear delayed Schrödinger equation ⋮ High-order structure-preserving Du Fort-Frankel schemes and their analyses for the nonlinear Schrödinger equation with wave operator

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