Charged particles 4 Geant4 simulation toolkit Numerical methods 4 Quantized state systems 4 Computational costs 2 Discrete event driven 2 Equations of motion 2 High energy physics 2 Intersection points 2 Iterative algorithm 2 Iterative methods 2 Magnetic fields 2 Nonuniform magnetic fields 2 Ordinary differential equation (ODE) 2 Ordinary differential equations 2 Particle transportation 2 Particle-matter interactions 2 Performance comparison 2 Polynomial segments 2 Quantization-based methods 2 Runge Kutta methods 2 Transportation 2 Uniform magnetic fields 2