This paper is concerned with the numerical stability of Runge-Kutta methods for a class of nonlinear functional differential and functional equations. The sufficient conditions for the stability and asymptotic stability of -algebraically stable Runge-Kutta methods are derived. A numerical test is given to confirm the theoretical results.
"Stability Analysis of Runge-Kutta Methods for Nonlinear Functional Differential and Functional Equations." J. Appl. Math. 2014 1 - 9, 2014. https://doi.org/10.1155/2014/607827