The Parker-Sochacki method delivers 4 to 13 orders of magnitude better kinetic energy conservation than Runge-Kutta methods for charged particle motion in static magnetic fields while running faster at matched accuracy.
Stiffness and Nonstiff Differential Equation Solvers, II: Detecting Stiffness with Runge–Kutta Methods
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High-Accuracy Numerical Solutions of Particle Motion in Static Magnetic Fields
The Parker-Sochacki method delivers 4 to 13 orders of magnitude better kinetic energy conservation than Runge-Kutta methods for charged particle motion in static magnetic fields while running faster at matched accuracy.