间断动力学系统实时仿真的分段组合算法

对于含有间断动力学系统的实时仿真问题，由于间断点的不确定性和实时仿真的快速性，无法直接采用定步长和变步长RK方法以及一般非实时间断仿真算法进行处理。针对间断点采用四阶实时连续RK公式进行预估和对间断区间进行平均分段处理的思想，构造并且研究了实时间断处理的分段组合算法．在舍间断点的分段区间上采用新的加权值法，其余分段区间应用不同阶次的实时RK公式，可以有效地提高实时仿真的精度。数值实验的结果表明该算法是有效可行的。

Piecewise Combining Algorithm for Real-time Simulation of Dynamic Systems with Discontinuities

As the discontinuous points are always uncertain in the simulation of dynamic systems with discontinuities and the quickness is necessary for real-time simulation,it is unsuitable to use RK methods with fixed step-size or variable step-size,and some other algorithms for discontinuity treating in non-real-time simulation.To forecast discontinuous points with the fourth order real-time continuous RK formula and to deal with averagely discontinuous regions,a piecewise combining algorithm for real-timely treating discontinuities was proposed.In the subsection regions containing discontinuous points,a new weighting method was applied,while in the others not containing discontinuous points real-time RK formulae with different orders were used,the accuracy of real-time simulation could be improved.The results of numerical experiments show that the algorithm is feasible and effective.