使用Jury准则对时域有限差分算法进行稳定性分析

摘要

Stability analysis is very important for the application of finite-difference time-domain （FDTD） methods. However, to find out all roots of a characteristic polynomial in stability analysis of the FDTD methods is a very difficult task, especially for high-order accurate FDTD methods. The Jury test in automatic control theory is introduced in detail, which only uses those coefficients of the characteristic polynomial for stability analysis instead of directly solving it. Such treatment can simplify the procedure of stability analysis. The Jury test is successfully applied in stability analysis of two typical FDTD methods.%在分析过程中要找出对应特征多项式的所有的根是相当困难的，尤其是对于高阶算法而言。为了解决这个问题，控制领域中的Jury准则将被引入，它仅需要使用特征多项式的系数而不需要直接求解整个方程获得所有的根。因此，使用它可以简化算法的稳定性分析，2个实例验证了它的有效性。