Symmetric multistep methods for charged-particle dynamics

Abstract

Abstract.A class of explicit symmetric multistep methods is proposed for integrating the equations of motion of charged particles in an electro-magnetic field. The magnetic forces are built into these methods in a special way that respects the Lagrangian structure of the problem. It is shown that such methods approximately preserve energy and momentum over very long times, proportional to a high power of the inverse stepsize. We explain this behaviour by studying the modified differential equation of the methods and by analysing the remarkably stable propagation of parasitic solution components.Math. classification. 65L06, 65P10, 78A35, 78M25.

Efficient energy-preserving methods for charged-particle dynamics

“…Remark 4.2 According to this result, it is known that the order of the Gauss-Legendre's quadrature using in (15) does not influence the long time momentum conservation. This point can be seen from the numerical results given in Section 5.…”

“…• EP3: the three-stage EP method (15) presented in this paper using the three-point Gauss-Legendre's quadrature.…”

“…A large amount of work in the literature has been devoted to studying the following charged-particle dynamics (see, e.g. [1,2,6,10,14,15,17,26,27,33])…”

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

“…As an illustrative numerical experiment, we consider the charged particle system of [14] with a constant magnetic field and an additional factor 1/ǫ. The system can be given by (1) with the potential U (x) = We consider applying four-point Gauss-Legendre's rule to the integral of the EEP integrator (5).…”

“…The Boris method was presented in [2] and it was researched further in [8,13,26]. Various other kinds of methods have also been researched for charged-particle dynamics, such as volume-preserving algorithms in [17], symplectic or K-symplectic algorithms in [18,29,33,35], and symmetric multistep methods in [14]. It is worth mentioning that, more recently, a variational integrator has been studied in [15] for solving charged-particle dynamics in a strong magnetic field.…”