We consider delay differential equations with a polynomially distributed delay. We derive an equivalent system of delay differential equations, which includes just two discrete delays. The stability of the equivalent system and its stationary solutions are investigated. Alternatively, a Gaussian quadrature generates a discretisation of the integral, which describes the distributed delay in the original delay differential equation. This technique yields an approximate differential equation with multiple discrete delays. We present results of numerical computations, where initial value problems of the differential equations are solved. Therein, the two approaches are compared.

翻译：我们研究了具有多项式分布时滞的时滞微分方程。我们推导出一个仅包含两个离散时滞的等价时滞微分方程组。研究了该等价系统的稳定性及其稳态解。作为替代方案，高斯求积法可生成描述原时滞微分方程中分布时滞的积分项的离散化。该技术产生了一个具有多个离散时滞的近似微分方程。我们给出了求解微分方程初值问题的数值计算结果，并对两种方法进行了比较。