In this paper, we investigate highly stable multistep Runge–Kutta methods for Volterra integral equations. First, the order conditions for order p and stage order \(q=p\) are presented, and a convergence theorem is given. The numerical stability conditions for the basic and convolution test equations are derived. Then, the methods with one or two stages are studied in detail. Some A-stable and \(V_0\)-stable m-stage methods with order \(p>m\) are obtained. For one-stage methods, we also construct \(A_0\)-stable and

中文翻译：

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Volterra积分方程的高度稳定的多步Runge–Kutta方法

在本文中，我们研究了用于Volterra积分方程的高度稳定的多步Runge-Kutta方法。首先，给出了阶数p和阶段阶数\（q = p \）的阶数条件，并给出了一个收敛定理。推导了基本和卷积测试方程的数值稳定性条件。然后，详细研究了一个或两个阶段的方法。一些甲-stable和\（V_0 \） -stable米-工段用顺序方法\（P>米\）获得。对于一阶段方法，我们还构造\（A_0 \）- stable和