关于微分-代数系统的Runge-Kutta迭代方法的研究

Research on Iterative Runge-Kutta Methods for DAEs

为了求解非自制指标-1的微分-代数系统,我们研究基于Runge-Kutta方法的动力学迭代过程,得到相关的非线性微分-代数方程的收敛理论,这类迭代过程具有一般性和灵活性,且沿着时间域网格点可以选取不同的插值函数。

This paper investigates a few form of Runge-Kutta formulae attaching waveform relaxation methods for solving nonautonomous differential-algebraic equations of index-1. The convergence of iterative Runge-Kutta formulae is verified for differential-algebraic equations of index-1. The proposed iterative processes are very general and even allow the inclusion of different interpolation formulae along the meshes.