延时微分方程多步Runge-Kutta方法的P-稳定性(英文)

The P─stability of Multistep Runge─Kutta Methods for Dalay Differential Equations

用多步Runse－Kutta方法去解如下形式的试验方程其中y（t）＝（y1（t），y2（t），…，yN（t））T，L和M是复N×N矩阵，τ＞0，Φ（t）是一个已知向量函数，当t≥0时y（t）是未知的．主要解决了延时微分方程多步Runge－Kutta方法的P－稳定性．

In this paper, we deal with the P-stability of Multistep Implicit Runge-Kutta Methods (MIRK ) for the numerical solution of systems of delay differential equations. We focus on the stability behaviour of MIRK in the solution of the following testsystems with a delay term: y' (t) = Ly (t) + My (t-T), t≥0. y (t) = Φ(t), t ≤0.Where y (t) = (y1 (t),y2(t), …,yN (t) )T, L and M are constant complex N ｘ N matrices, T τ≥0, Φ(t) denotes a given vector value function and y (t) is unknown for t ≥0.