Guiding Center 4d Barely Passing with Gauss-Legendre VPRK Methods and Projections
The time step and number of time steps are those of this orbit, set in src/guiding-center-4d.jl; the toroidal momentum is shown alongside the energy, as the second invariant of the guiding centre dynamics.
VPRKGauss(1)
SymplecticGauss(1) with standard projection
SymplecticGauss(1) with symmetric projection
SymplecticGauss(1) with symplectic projection
SymplecticGauss(1) with midpoint projection
SymplecticGauss(1) with internal stage projection
Simulation crashed after 0 of 12500 time steps: MethodError.
VPRKGauss(2)
SymplecticGauss(2) with standard projection
SymplecticGauss(2) with symmetric projection
SymplecticGauss(2) with symplectic projection
SymplecticGauss(2) with midpoint projection
SymplecticGauss(2) with internal stage projection
Simulation crashed after 0 of 12500 time steps: MethodError.
VPRKGauss(3)
SymplecticGauss(3) with standard projection
SymplecticGauss(3) with symmetric projection
SymplecticGauss(3) with symplectic projection
SymplecticGauss(3) with midpoint projection
SymplecticGauss(3) with internal stage projection
Simulation crashed after 0 of 12500 time steps: MethodError.
VPRKGauss(4)
SymplecticGauss(4) with standard projection
SymplecticGauss(4) with symmetric projection
SymplecticGauss(4) with symplectic projection
SymplecticGauss(4) with midpoint projection
SymplecticGauss(4) with internal stage projection
Simulation crashed after 0 of 12500 time steps: MethodError.
VPRKGauss(5)
SymplecticGauss(5) with standard projection
SymplecticGauss(5) with symmetric projection
SymplecticGauss(5) with symplectic projection
SymplecticGauss(5) with midpoint projection
SymplecticGauss(5) with internal stage projection
Simulation crashed after 0 of 12500 time steps: MethodError.
VPRKGauss(6)
SymplecticGauss(6) with standard projection
SymplecticGauss(6) with symmetric projection
SymplecticGauss(6) with symplectic projection
SymplecticGauss(6) with midpoint projection
SymplecticGauss(6) with internal stage projection
Simulation crashed after 0 of 12500 time steps: MethodError.