2026/07/23 by Zhihao Qi, Weibing Deng · 1 citation
#math.NA #cs.NA
This paper considers a class of charged-particle dynamics problems in which the particle is subjected to a magnetic force, with a magnetic flux density inversely proportional to a small parameter 0<ε≪ 1, and a nonlinear electric force. The resulting highly oscillatory behavior poses significant challenges for numerical computation. To enhance the performance of exponential integrators (EIs), this paper employs a technique that linearizes the ordinary differential equation through a dimension-raising approach. Based on this technique, a new family of EIs is developed that achieves arbitrarily high order. For short-time simulations on the interval [0,T], it is rigorously proved that the proposed method--which employs auxiliary polynomials of degree k and a time step Δt--satisfies two distinct error bounds: O(ε Δtk+1) and O(εk+2). The latter bound guarantees that the algorithm stays accurate even when the step size is of order O(1). Furthermore, when a large step size ε-1Δt is used to simulate the long-term dynamics over [0,ε-1T], the numerical scheme attains a uniform convergence rate of O(Δtk+1). Several numerical experiments confirm these theoretical results.