Split-step spectral schemes for nonlinear Dirac systems
Journal of Computational Physics
Linearized Crank-Nicholson scheme for nonlinear Dirac equations
Journal of Computational Physics
A first course in the numerical analysis of differential equations
A first course in the numerical analysis of differential equations
Multi-symplectic Runge-Kutta collocation methods for Hamiltonian wave equations
Journal of Computational Physics
Geometric integrators for the nonlinear Schrödinger equation
Journal of Computational Physics
Multi-symplectic Runge-Kutta methods for nonlinear Dirac equations
Journal of Computational Physics
Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems
Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems
Mathematical and Computer Modelling: An International Journal
Multi-symplectic Runge-Kutta methods for nonlinear Dirac equations
Journal of Computational Physics
An efficient adaptive mesh redistribution method for a non-linear Dirac equation
Journal of Computational Physics
Journal of Computational Physics
Explicit multi-symplectic methods for Klein-Gordon-Schrödinger equations
Journal of Computational Physics
Symplectic integrator for nonlinear high order Schrödinger equation with a trapped term
Journal of Computational and Applied Mathematics
Splitting multisymplectic integrators for Maxwell's equations
Journal of Computational Physics
High-order compact splitting multisymplectic method for the coupled nonlinear Schrödinger equations
Computers & Mathematics with Applications
Symplectic and multisymplectic numerical methods for Maxwell's equations
Journal of Computational Physics
Explicit multi-symplectic extended leap-frog methods for Hamiltonian wave equations
Journal of Computational Physics
Solvability of concatenated Runge-Kutta equations for second-order nonlinear PDEs
Journal of Computational and Applied Mathematics
Local structure-preserving algorithms for the "good" Boussinesq equation
Journal of Computational Physics
Journal of Computational Physics
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In this paper, we consider the multi-symplectic Runge-Kutta (MSRK) methods applied to the nonlinear Dirac equation in relativistic quantum physics, based on a discovery of the multi-symplecticity of the equation. In particular, the conservation of energy, momentum and charge under MSRK discretizations is investigated by means of numerical experiments and numerical comparisons with non-MSRK methods. Numerical experiments presented reveal that MSRK methods applied to the nonlinear Dirac equation preserve exactly conservation laws of charge and momentum, and conserve the energy conservation in the corresponding numerical accuracy to the method utilized. It is verified numerically that MSRK methods are stable and convergent with respect to the conservation laws of energy, momentum and charge, and MSRK methods preserve not only the inner geometric structure of the equation, but also some crucial conservative properties in quantum physics. A remarkable advantage of MSRK methods applied to the nonlinear Dirac equation is the precise preservation of charge conservation law.