Gauss-Legendre求积公式在系统仿真中的应用

The Application of Gauss-Legendre Quadrature Formulas in System Simulation

本文将Gauss-Legendre求积公式应用到线性定常系统的快速仿真中,提出了一种新方法。在以保持A-稳定性为前提使每步仿真计算量为最小的意义下,它是最优的。该方法与现有同阶方法相比,其截断误差系数也较小,并具有L-稳定性,因而特别适合于Stiff系统的仿真。文中还讨论了实时问题。

In this paper, Gauss-Legendre quadrature formulas are used in the fast simulation of linear time-invariant systems and a new method is proposed. The method is optimal in the sense that under the condition of keeping A-stability it occurs the least computational overhead in every simulation step. Compared with the other methods of the same accuracy order, its coefficient of truncation error is smaller also and moreover the method is L-stable, thus it is very suitable for the simulation of stiff systems. Real-time problem is discussed in the paper as well.