AI 中文总结
研究强非恒定磁场下三维带电粒子动力学模型，通过核 - 值域分解等构建曲线参考指数积分器（CREI），证明其误差界并给出数值实验，在 h 收敛性和 ε 一致性方面有贡献。
AI 中文摘要
我们研究了非相对论动量表述下的三维带电粒子动力学模型，并为该系统构建了曲线参考指数积分器（CREI）。由于线性部分的零特征值不是半单的，常规变量变换后的系统不满足经典局部线性化扩展指数积分器（LLEEI）中使用的谱条件。主导磁矩阵的核 - 值域分解和进一步的线性变换将方程简化为具有半单零块和一个常数斜对称振荡块的系统。CREI 沿精确振荡曲线而非固定点展开非线性项。保留到 k 次单项式定义了 CREI(k + 1)。我们证明了一致的局部和全局误差界，并给出了关于 h 收敛性和 ε 一致性的可重复数值实验。
英文摘要
We study a three-dimensional charged-particle dynamics model in the nonrelativistic momentum formulation and construct a curve-reference exponential integrator (CREI) for this system. Since the zero eigenvalue of linear section is not semisimple, the system after usual change of variables does not meet the spectral condition used in the classical locally linearized extended exponential integrator (LLEEI). A kernel-range decomposition of the dominant magnetic matrix and a further linear transformation reduce the equation to a system with a semisimple zero block and one constant skew-symmetric oscillatory block. The CREI expands the nonlinear term along the exact oscillatory curve rather than at a fixed point. Retaining monomials through degree k defines CREI(k + 1). We prove uniform local and global error bounds and present reproducible numerical experiments for convergence in h and uniformity in ε.
