Abstract For the numerical solution of the Cauchy problem with multiple poles, we propose a reciprocal function method. In the case of first-order poles, it makes it possible to continue the solution through the poles and to determine the solution and the pole positions with good accuracy. The method allows one to employ conventional explicit and implicit schemes, for example, explicit Runge–Kutta schemes. A test problem with multiple poles is computed as an example. The proposed method is useful for construction of software for direct computation of special functions.

中文翻译：

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具有一阶极点的柯西问题的倒数函数方法

摘要 针对多极点柯西问题的数值解，我们提出了倒数函数法。在一阶极点的情况下，可以通过极点继续求解，并以良好的精度确定解和极点位置。该方法允许使用传统的显式和隐式方案，例如显式 Runge-Kutta 方案。以计算具有多个极点的测试问题为例。所提出的方法对于构建用于直接计算特殊函数的软件很有用。