Nonlinear stability and D-convergence of Runge-Kutta methods for delay differential equations
Stability and convergence of Runge-Kutta methods with Lagrangian interpolation applied to nonlinear ordinary delay differential equations are studied. The new concepts of strong algebraic stability, GDN-stability and D-convergence are introduced to facilitate the analysis. A correspondence between certain stability properties of Runge-Kutta methods applied to ordinary differential equations and relevant stability properties of the same methods enhanced by Lagrangian interpolation and applied to delay differential equations is established.
scientific article; zbMATH DE number 1100611