非自治脉冲微分系统的数值稳定性

Numerical stability of non-autonomous impulsive differential systems

研究非自治脉冲微分方程{x(t)=a(t)x(t),t≠i,t>i0x(t+)=μx(t),t=i x(i+0)=x0通过数值实验发现,在a(t)→-∞,t→+∞的条件下,显式Euler方法和隐式Euler方法的数值稳定性与应用于自治线性脉冲微分方程时的结论截然相反。对此结论给出了严格的理论证明,并在此基础上讨论单腿θ-方法的数值稳定性,给出不同条件下,单腿θ-方法数值稳定的θ的取值范围。

For non-autonomous impulsive differential equations（ IDEs）{x（ t） = a（ t） x（ t）,t≠i,t i0x（ t＋） = μx（ t）,t = i x（ i＋0） = x0with a（ t） →- ∞,t→ ＋ ∞,it is found from some numerical counter-examples that the stability results of the explicit and implicit Euler methods are quite different from those obtained by applying them to the autonomous linear IDEs. Then this is proved theoretically,and thereby,the numerical stability of one-legθ-methods is studied and the stability region of θ is given under different stability conditions of the underlying equations.