A modification of the standard Boris algorithm, called filtered Boris algorithm, is proposed for the numerical integration of the equations of motion of charged particles in a strong non-uniform magnetic field in the asymptotic scaling known as maximal ordering. With an appropriate choice of filters, second-order error bounds in the position and in the parallel velocity, and first-order error bounds in the normal velocity are obtained with respect to the scaling parameter. This also yields a second-order approximation to the guiding center motion. The proof compares the modulated Fourier expansions of the exact and the numerical solutions. Numerical experiments illustrate the error behaviour of the filtered Boris algorithm.

中文翻译：

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强磁场中带电粒子动力学的滤波 Boris 算法

提出了标准 Boris 算法的一种修改，称为过滤 Boris 算法，用于在称为最大排序的渐近缩放中对强非均匀磁场中带电粒子的运动方程进行数值积分。通过选择适当的滤波器，位置和平行速度中的二阶误差界限以及法向速度中的一阶误差界限相对于缩放参数获得。这也产生了引导中心运动的二阶近似。证明比较了精确解和数值解的调制傅立叶展开。数值实验说明了滤波鲍里斯算法的错误行为。