An improvement of the numerical stability results for nonlinear neutral delay-integro-differential equations

This paper deals with stability of the extended Runge-Kutta methods for nonlinear neutral delay-integro-differential equations. The stability results in the reference [Y. Yu, L. Wen, S. Li, Nonlinear stability of Runge-Kutta methods for neutral delay integro-differential equations, Appl. Math. Comput. 191 (2007) 543-549] are improved. With this improvement, several new numerical stability criteria are obtained, it is proven that the extended Runge-Kutta methods are globally and asymptotically stable under the suitable conditions.