High-order compact methods for the nonlinear Dirac equation

DOI10.1007/S40314-018-0705-4zbMath1413.65325OpenAlexW2889260401MaRDI QIDQ1715705

Xiang-Gui Li, Shu-Cun Li

Publication date: 29 January 2019

Published in: Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40314-018-0705-4

zbMATH Keywords

random perturbationcompact difference schemenonlinear Dirac equationcollision of solitary waves

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Wave equation (35L05) 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) Computational methods for problems pertaining to quantum theory (81-08) Perturbations in context of PDEs (35B20) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Direct numerical methods for linear systems and matrix inversion (65F05) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (10)

High-order conservative schemes for the nonlinear Dirac equation ⋮ High-order numerical methods with mass and energy conservation for spin–orbit-coupled Bose–Einstein condensates ⋮ Convergence analysis of two conservative finite difference Fourier pseudo-spectral schemes for Klein-Gordon-Dirac system ⋮ Error bounds of fourth‐order compact finite difference methods for the Dirac equation in the massless and nonrelativistic regime ⋮ Analysis of two conservative fourth-order compact finite difference schemes for the Klein-Gordon-Zakharov system in the subsonic limit regime ⋮ Optimal point-wise error estimate of two conservative fourth-order compact finite difference schemes for the nonlinear Dirac equation ⋮ Analysis of a conservative fourth-order compact finite difference scheme for the Klein-Gordon-Dirac equation ⋮ Three Discontinuous Galerkin Methods for One- and Two-Dimensional Nonlinear Dirac Equations with a Scalar Self-Interaction ⋮ Operator-compensation methods with mass and energy conservation for solving the Gross-Pitaevskii equation ⋮ Energy-preserving exponential integrator Fourier pseudo-spectral schemes for the nonlinear Dirac equation

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