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This paper is devoted to a study of nonlinear stability of general linear methods for the numerical solution of delay differential equations in Hilbert spaces. New stability concepts are further introduced. The stability properties of (k, p, q)-algebraically stable general linear methods with piecewise constant or linear interpolation procedure are investigated. We also discuss stability of linear multistep methods viewed as a special subset of the class of general linear methods. [ABSTRACT FROM AUTHOR]

This paper is concerned with the numerical solution of delay differential equations(DDEs). We focus on the stability behaviour of Runge-Kutta methods for nonlinear DDEs. The new concepts of GR(l)-stability, GAR(l)-stability and weak GAR(l)stability are further introduced. We investigate these stability properties for (k, l)algebraically stable Runge-Kutta methods with a piecewise constant or linear interpolation procedure. [ABSTRACT FROM AUTHOR]