多维分段连续型延迟微分方程的稳定性

摘要

This paper deals with the stability of high-dimensional differential equations with piece-wise continuous arguments.By using theθ-method ,we solved this class of differential equations with de-lay term [t].And using the unbounded maximum modulus principle,we proved its recursive expression is Schur polynomial.Thus,we get the stability result that whenθ∈[12 ,1],the method is stable.Finally, our conclusion are tested by examples in two-dimension and three-dimension.%本文主要研究多维分段连续型延迟微分方程数值解的稳定性。应用θ-方法解带有延迟项[t]的该类方程,利用无界区域最大模原理证明其递推式为舒尔多项式,从而得出θ-方法的稳定性结论：当θ∈[12,1]时是方法稳定的。最后分别用二维和三维情形的例子验证了结论的正确性。