Keywords: 35Q55; 34A33; 65P10; 65L20; Nonlinear Schrödinger; Weak turbulence; Conservative integrators;
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Energy-conserving methods for the nonlinear Schrödinger equation
Keywords: Hamiltonian partial differential equations; Nonlinear Schrödinger equation; Energy-conserving methods; Line integral methods; Hamiltonian Boundary Value methods; HBVMs; 65P10; 65M20; 65L05;
Analysis of Energy and QUadratic Invariant Preserving (EQUIP) methods
Keywords: 65P10; 65L05; Gauss collocation methods; Symplectic methods; Energy-conserving methods; Line integral methods; Hamiltonian problems; Poisson problems;
A class of energy-conserving Hamiltonian boundary value methods for nonlinear Schrödinger equation with wave operator
Keywords: Nonlinear Schrödinger equation; Hamiltonian problem; Wave operator; Energy-conserving methods; Hamiltonian boundary value methods; 65P10; 65N40;
Structure-preserving Galerkin POD reduced-order modeling of Hamiltonian systems
Keywords: 37M25; 65M99; 65P10; 93A15; Proper orthogonal decomposition; Model reduction; Hamiltonian systems; Structure-preserving algorithms;
Improving the accuracy of the AVF method
Keywords: 65P10; 65L12; 34K28Geometric numerical integration; Discrete gradient method; Average vector field method; Locally exact scheme; BB-series; Hamiltonian systems
Energy-preserving methods for Poisson systems
Keywords: 65P10; 65L05Ordinary differential equations; One-step methods; Poisson problems; Hamiltonian boundary value methods; Energy-preserving methods; Line integral methods
Lobatto IIIA–IIIB discretization of the strongly coupled nonlinear Schrödinger equation
Keywords: 65P10; 37K05; 37M15Nonlinear Schrödinger equation; Multi-symplectic integration; Lobatto IIIA–IIIB methods; Solitons
A discrete action principle for electrodynamics and the construction of explicit symplectic integrators for linear, non-dispersive media
Keywords: 65M12; 65P10; 65Z05; 70S05; 78M20Dispersion; Electrodynamics; FDTD; Lagrangian; Runge–Kutta; Stability; Symplectic integrator
VALIS: A split-conservative scheme for the relativistic 2D Vlasov–Maxwell system
Keywords: 65P10; 82D10Vlasov; Eulerian; Time-splitting; Piecewise Parabolic Method; Plasma; Raman
Geometric discrete analogues of tangent bundles and constrained Lagrangian systems
Keywords: 70G75; 49S05; 70F20; 70F25; 37J60; 70-08; 65P10; 37M15; 53Z05Geometric discretization; Holonomic and nonholonomic mechanics; Variational integrators
Delayed feedback control of chaotic spinning disk via minimum entropy approach
Keywords: 65P10; 37N35; 93B52; 94A17; 54C70Spinning disk; Chaos control; Minimum entropy; Delayed feedback
State-dependent symplecticity and area preserving numerical methods
Keywords: 65L05; 65P10; 37M15Hamiltonian systems; Poisson systems; Symplecticity; Runge–Kutta methods; Discrete gradient methods
Statistical mechanics of Arakawa’s discretizations
Keywords: 65M06; 65P10; 86A10; 82B99Conservative discretizations; Statistical mechanics; Geometric numerical integration; Quasi-geostrophic flow; Geophysical fluid dynamics
Discrete Lagrangian field theories on Lie groupoids
Keywords: 58A20; 58H05; 65P10; 70S05Discrete field theory; Lie groupoids; Lagrangian field theory; Discrete differential geometry
Hybrid solvers for composition and splitting methods
Keywords: 65L05; 65L06; 65P10; 68W30Geometric numerical integration; Composition methods; Splitting methods; Numerical differential equations
Almost symplectic Runge-Kutta schemes for Hamiltonian systems
Keywords: 65L05; 65L06; 65P10; Geometric integrators; Hamiltonian structure; Symplectic Runge-Kutta methods; Pseudo-symplecticity; Fixed-point iteration; Newton's method; Convergence;