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Highly stable multistep Runge–Kutta methods for Volterra integral equations
Computational and Applied Mathematics ( IF 2.5 ) Pub Date : 2020-11-01 , DOI: 10.1007/s40314-020-01351-z
Jiao Wen , Aiguo Xiao , Chengming Huang

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:

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-stable和\(V_0 \) -stable-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

更新日期:2020-11-02
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