具有最大稳定域的实时RK4公式

实时仿真通常要求计算机在一个动态循环中与外部硬件相互作用。外部数据必须从输入信号中采集，并融入到数值积分算法中以计算出状态变量。同样，从积分过程中求得的数据也必须及时被输出。因此，一般希望能选择较大的积分步长，以保证能有足够的计算时间。首先将实时四阶龙格-库塔公式的稳定域问题化为一个约束求极大值问题，利用优化方法，找到了具有最大稳定域的实时四阶龙格-库塔公式应满足的条件。然后，根据局部截断误差与相关系数的关系，将其化为一个约束求极小值问题，并最终导出了一个新的实时RK4公式。该公式不仅具有最大的稳定域，而且局部截断误差函数值也小于其它已知的实时RK4公式。仿真结果表明，该公式是有效可行的。

Real-time RK4 Formula with Maximum Stability Region

Real-time simulation often requires a computer to interact with external hardware in a dynamic loop. Data must be sampled from input signals and incorporated into the numerical integration algorithm to calculate the state variables. Also, data from the integration process must be output-ted in time. Thus, the ability for choosing a larger integration step-size is often demanded, so as to guarantee enough time for computation. The problem concerned with the stability region of real-time fourth-order Runge-Kutta formulae is converted into the one of restricted optimization for maximum, and the condition for maximum stability region of real-time fourth-order Runge-Kutta formulae is found. Also, based on the relation of local truncation error and related coefficients, a problem of restricted optimization for minimum is gotten, and a new real-time RK4 formula is deduced finally. The formula has not only maximum stability region, but also the function value of local truncation error which is smaller than the other known real-time RK4 formulae. The simulation results show that the proposed formula is feasible and effective.