一类秩2微分代数系统的并行Runge-Kutta方法

A Class of Parallel Runge-Kutta Methods for Differential-Algebraic Systems of Index 2

对多处理机系统构造了一类秩 2微分代数系统的并行Runge -Kutta方法。对该类方法给出了阶条件 ,并且研究了收敛性理论。还研究了Runge -Kutta解的存在性和唯一性。已经构造了一系列使定理 4中的假定成立的具体公式 ,并在飞行器的轨道仿真中应用 ,也提出了一些要进一步研究的问题。

A class of parallel Runge-Kutta methods for differential-algebraic equations of index 2 are constructed for multiprocessor system. This paper gives the order conditions and investigtes the convergence theory for such methods. The existence and uniqueness of the Runge-Kutta solution are also studied. A sequence of concrete formulas have been constructed which satisfy the assumptions of Theorem 4, and these formulas have been applied in the trajectory simulation of the vebicles. Some problems that will be studied furthermore are also presented.\;