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)
Simulation crashed after 4457 of 12500 time steps: solver error – non-finite direction vector.
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)
Simulation crashed after 4823 of 12500 time steps: solver error – non-finite direction vector.
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)
Simulation crashed after 8233 of 12500 time steps: solver error – non-finite direction vector.
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)
Simulation crashed after 10469 of 12500 time steps: solver error – non-finite direction vector.
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.