We consider the scalar autonomous initial value problem as solved by an explicit Runge-Kutta pair of orders 6 and 5. We focus on an efficient family of such pairs, which were studied extensively in previous decades. This family comes with 5 coefficients that one is able to select arbitrarily. We set, as a fitness function, a certain measure, which is evaluated after running the pair in a couple of relevant problems. Thus, we may adjust the coefficients of the pair, minimizing this fitness function using the differential evolution technique. We conclude with a method (i.e. a Runge-Kutta pair) which outperforms other pairs of the same two orders in a variety of scalar autonomous problems.

中文翻译：

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用于推导针对标量自治问题调整的 Runge-Kutta 对的神经网络技术

我们认为标量自治初始值问题是由 6 阶和 5 阶的显式 Runge-Kutta 对解决的。我们专注于此类对的有效族，这些对在过去的几十年中得到了广泛的研究。该系列带有 5 个可以任意选择的系数。我们将某个度量设置为适应度函数，在几个相关问题中运行该对后对其进行评估。因此，我们可以调整对的系数，使用差分进化技术最小化这个适应度函数。我们以一种方法（即 Runge-Kutta 对）作为结论，该方法在各种标量自治问题中优于其他具有相同两个阶数的对。