The present paper is concerned with the relationship between stepsize restriction and nonlinear stability of Runge-Kutta methods for delay differential equations. We obtain a special stepsize condition guaranteeing global and asymptotical stability properties of numerical methods. Some confirmations of the conditions on Runge-Kutta methods are illustrated at last.
"Stepsize Restrictions for Nonlinear Stability Properties of Neutral Delay Differential Equations." Abstr. Appl. Anal. 2014 (SI40) 1 - 7, 2014. https://doi.org/10.1155/2014/304071