中立型延迟微分方程Runge-Kutta方法的稳定性

摘要

研究以下中立型延迟微分方程y'(t)=Ly(t)+My(t-τ1)+Ny'(t-τ2) t≥0y(t)=g(t) t＜0其中L,M,N是d×d复矩阵,τ2≥τ1＞0,g(t)是给定的向量函数.证明了Runge-Kutta法是NGP-稳定的充分必要条件是它是A-稳定的.%Consider the following neutral delay differential equation (NDDE)y'(t) = Ly(t) + My(t- τ1) + Ny'(t - τ2) t ≥ 0y(t) = g(t) t ＜ 0where L, M, N are d× d complex matrixs. τ2≥τ1＞0. g(t) is a given vector function. The Runge-Kutta methods is NGP-stable if and only if it is A-stable, when used to the test system above.