Delay differential equations have been used to model numerous phenomena in nature. We extend the previous work of one of the authors to analyze the stability properties of the explicit exponential Rosenbrock methods for stiff differential equations with constant delay. We first derive sufficient conditions so that the exponential Rosenbrock methods satisfy the desired stability property. We accomplish this without relying on some extreme constraints, which are usually necessary in stability analysis. Then, with the aid of the integral form of the method coefficients, we provide a simple stability criterion that can be easily verified. We also present a theorem on the order barrier for the proposed methods, stating that there is no method of order five or higher that satisfies the simple criterion. Numerical tests are carried out to validate the theoretical results.

中文翻译：

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常时滞刚性微分方程显式指数Rosenbrock方法的稳定性分析


时滞微分方程已被用来模拟自然界中的许多现象。我们扩展了其中一位作者之前的工作，分析了具有恒定延迟的刚性微分方程的显式指数 Rosenbrock 方法的稳定性特性。我们首先推导出足够的条件，使指数 Rosenbrock 方法满足所需的稳定性。我们在不依赖一些极端约束的情况下实现了这一点，这在稳定性分析中通常是必要的。然后，借助方法系数的积分形式，我们提供了一个易于验证的简单稳定性准则。我们还提出了关于所提出方法的阶数障碍的定理，指出不存在满足简单标准的五阶或更高阶方法。进行数值测试以验证理论结果。