Volume 57, Number 4, July-August 2023
|Page(s)||2427 - 2450|
|Published online||18 July 2023|
Semi-discretization and full-discretization with improved accuracy for charged-particle dynamics in a strong nonuniform magnetic field
School of Mathematics and Statistics, Xi’an Jiaotong University, 710049 Xi’an, P.R. China
* Corresponding author: email@example.com
Accepted: 20 June 2023
The aim of this paper is to formulate and analyze numerical discretizations of charged-particle dynamics (CPD) in a strong nonuniform magnetic field. A strategy is firstly performed for the two dimensional CPD to construct the semi-discretization and full-discretization which have improved accuracy. This accuracy is improved in the position and in the velocity when the strength of the magnetic field becomes stronger. This is a better feature than the usual so called ``uniformly accurate methods”. To obtain this refined accuracy, some reformulations of the problem and two-scale exponential integrators are incorporated, and the improved accuracy is derived from this new procedure. Then based on the strategy given for the two dimensional case, a new class of uniformly accurate methods with simple scheme is formulated for the three dimensional CPD in maximal ordering case. All the theoretical results of the accuracy are numerically illustrated by some numerical tests.
Mathematics Subject Classification: 65L05 / 65L70 / 78A35 / 78M25
Key words: Charged particle dynamics / improved accuracy / strong nonuniform magnetic field / high oscillations / two-scale exponential integrators
© The authors. Published by EDP Sciences, SMAI 2023
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