We describe a practical algorithm for computing the Stokes multipliers of a linear differential equation with polynomial coefficients at an irregular singular point of single level one. The algorithm follows a classical approach based on Borel summation and numerical ODE solving, but avoids a large amount of redundant work compared to a direct implementation. It applies to differential equations of arbitrary order, with no genericity assumption, and is suited to high-precision computations. In addition, we present an open-source implementation of this algorithm in the SageMath computer algebra system and illustrate its use with several examples. Our implementation supports arbitrary-precision computations and automatically provides rigorous error bounds. The article assumes minimal prior knowledge of the asymptotic theory of meromorphic differential equations and provides an elementary introduction to the linear Stokes phenomenon that may be of independent interest.

翻译：本文描述了一种实用算法，用于计算多项式系数线性微分方程在单层一级不规则奇点处的斯托克斯乘子。该算法遵循基于Borel求和与数值常微分方程求解的经典方法，但与直接实现相比避免了大量冗余计算。该算法适用于任意阶微分方程，无需一般性假设，且适合高精度计算。此外，我们在SageMath计算机代数系统中提供了该算法的开源实现，并通过多个示例说明其使用方法。我们的实现支持任意精度计算，并能自动提供严格的误差界。本文假设读者仅具备亚纯微分方程渐近理论的基础知识，并对线性斯托克斯现象提供了可独立参考的初等介绍。