Exponential energy-preserving methods for charged-particle dynamics in a strong and constant magnetic field

Abstract

In this paper, exponential energy-preserving methods are formulated and analysed for solving charged-particle dynamics in a strong and constant magnetic field. The resulting method can exactly preserve the energy of the dynamics. Moreover, it is shown that the magnetic moment of the considered system is nearly conserved over a long time along this exponential energy-preserving method, which is proved by using modulated Fourier expansions. Other properties of the method including symmetry and convergence are also studied. An illustrated numerical experiment is carried out to demonstrate the long-time behaviour of the method.

References in corpus (3)

• Exponential integrators preserving first integrals or Lyapunov functions for conservative or dissipative systems
• Trigonometric collocation methods based on Lagrange basis polynomials for multi-frequency oscillatory second-order differential equations
• Explicit symplectic algorithms based on generating functions for charged particle dynamics