This paper presents a new discretization error quantification method for the numerical integration of ordinary differential equations. The error is modelled by using the Wishart distribution, which enables us to capture the correlation between variables. Error quantification is achieved by solving an optimization problem under the order constraints for the covariance matrices. An algorithm for the optimization problem is also established in a slightly broader context.

翻译：本文提出了一种针对常微分方程数值积分的离散化误差量化新方法。该误差通过Wishart分布进行建模，从而能够捕捉变量之间的相关性。通过在协方差矩阵的阶约束条件下求解优化问题，实现了误差的量化。此外，本文还在稍广义的框架下建立了该优化问题的求解算法。