A quantitative definition of numerical stiffness for initial value problems is proposed. Exponential integrators can effectively integrate linearly stiff systems, but they become expensive when the linear coefficient is a matrix, especially when the time step is adapted to maintain a prescribed local error. Schur decomposition is shown to avoid the need for computing matrix exponentials in such simulations, while still circumventing linear stiffness.

翻译：本文提出了一种针对初值问题数值刚性的定量定义。指数积分器能够有效积分线性刚性系统，但当线性系数为矩阵时，特别是为保持指定局部误差而调整时间步长时，其计算成本会变得高昂。研究表明，舒尔分解可在避免此类模拟中计算矩阵指数需求的同时，仍能规避线性刚性问题。