Stability and Dissipativity of Multistep Runge–Kutta Methods for Nonlinear Delay Differential Equations with Constrained Grid

This paper is devoted to the stability and dissipativity of multistep Runge–Kutta methods with constrained grid for a class of nonlinear neutral delay differential equations. Nonlinear stability and dissipativity are introduced and proved. We discuss both the \( GR(l) \)-stability, \( GAR(l) \)-stability, and the weak \( GAR(l) \)-stability on the basis of \( (k,l) \)-algebraically stable of the multistep Runge–Kutta methods, we also prove that an algebraically stable, irreducible multistep Runge–Kutta method is finite-dimensional dissipative.