延迟微分方程隐-显式线性多步法的稳定性

Stability of Implicit-explicit Linear Multi-step Methods for Delay Differential Equation

通过研究延迟微分方程隐-显式线性多步法的稳定性,给出两类特殊的隐-显式方法即隐-显式Euler方法和隐-显式BDF方法的稳定性结论,证明了隐-显式Euler方法是P-稳定的,隐-显式BDF方法不是P-稳定的。为了克服边界轨迹法刻画复空间稳定区域的困难,给出了一种新的复空间上稳定区域的刻画方法,并用这种方法给出了隐-显式BDF方法的数值稳定性区域的描述,最后通过数值算例验证了这种刻画稳定区域的方法的可行性。

Through studying the stability of implicit-explicit multi-step methods for the delay differential equations,the stability of two kinds of methods such as implicit-explicit Euler methods and implicit-explicit BDF methods were proposed.It is proved that the implicit-explicit Euler method is P-stable and the implicit-explicit BDF methods is not P-stable.To deal with the difficulty of describing the stability region in complex space by boundary locus techniques,a new description method of stability region was proposed and was applied to the implicit-explicit BDF methods.Numerical experiments show that the new description method is effective.