延迟系统的并行BDF算法及其稳定性分析

Parallel BDF Algorithms for Delay Systems with Stability Analysis

以显式BDF方法为预估式 ,以隐式BDF方法为校正式构造了一类求解延迟系统的并行BDF算法 .探讨了算法的稳定性 ,得到了算法渐进稳定的一个充分条件 ,导出了该算法的稳定性是由相应的常微系统(ODEs)的方法的稳定性控制的 .理论分析和数值试验表明 。

This paper constructs a class of parallel BDF algorithms for the systems of delay differential equations with explicit BDF methods as predictor and implicit BDF methods as corrector. In the paper the stability analysis is discussed, and a sufficient condition under which the systems of delay differential equations are asymptotically stable is derived. It is easily inferred that the stability of the algorithm is controlled by the stability of the corresponding ordinary differential equations. Some results of numerical tests are also presented. From theoretical analysis and numerical tests the conclusion can be drawn that the algorithm is not only for linear problems, but also for nonlinear problems.