延迟微分方程单支方法的非线性稳定性

NONLINEAR STABILITY OF ONE-LEG METHODS FOR DELAY DIFFERENTIAL EQUATIONS

本文讨论延迟微分方程单支方法的非线性稳定性 .对于 Kα,β,γ类非线性延迟微分方程 ,我们证明带有线性插值的 G( c,p,q) -代数稳定的单支方法当 c≤ 1时是 GR( p/2 ,q/2 ) -稳定及弱 GAR( p/2 ,q/2 ) -稳定的 ,当 c<1时是 GAR( p/2 ,q/2 ) -稳定的 .最后的数值试验表明了上述结论的正确性 .

In this paper, we discuss the nonlinear stability of G(c,p,q)-algebraically stable one-leg methods for delay differential equations(DDEs) of the class K α,β,γ. We prove that G(c,p,q)-algebraically stable one-leg methods with linear interpolation are GR(p/2,q/2)-stable and weak GAR(p/2,q/2)-stable for c≤1, and GAR(p/2,q/2)-stable for c<1. At the end of this paper, some numerical experiments are given, which confirm the theoretical results.