Numerical stability of solution to delay differential equations under resolvent condition for Runge-Kutta methods

Deals with the application of Kreiss resolvent condition in the error growth analysis of numerical methods, and studies the stability of Runge-Kutta method in respect of Kreiss resolvent condition with emphasis on the study on the subclass of collocation methods with abscissas in [ 0,1 ] by applying the methods to the test equation U＇(t) = λ U(t) + μU( t - τ)τ ＞ 0 with complex constraintsμ and λ, and proves under some assumptions on the R-K methods that the error growth is uniformly bounded in the stability region.