An Explicit Symmetric Exponential Integrator and Its Error Estimate for the Relativistic Charged-Particle Dynamics
This provides an efficient numerical method for simulating relativistic charged particles in magnetic fields, which is incremental as it builds on existing splitting techniques.
The paper tackled the simulation of relativistic charged-particle dynamics by constructing an explicit symmetric exponential integrator, achieving unconditional stability and second-order convergence with superior accuracy, efficiency, and long-time Hamiltonian conservation in numerical experiments.
This paper investigates the equations of motion for a relativistic charged particle in a general magnetic field. By reformulating the dynamics in four-dimensional spacetime and separating the linear and nonlinear parts, we construct an explicit symmetric exponential integrator based on Lie splitting. Rigorous analysis establishes its unconditional stability and second-order convergence. Numerical experiments confirm its superior performance, including accuracy, effciency and long-time Hamiltonian conservation.