\(GP_k\)-stability of multistep Runge-Kutta methods for a class of multidelay systems. (English) Zbl 0998.65076
Summary: This paper deals with the asymptotic stability of multistep Runge-Kutta methods for a class of multidelay systems. It is shown that \(A\)-stability of multistep Runge-Kutta methods for ordinary differential equations is equivalent to \(\text{GP}_k\)-stability of the induced methods for the multidelay systems.
MSC:
| 65L20 | Stability and convergence of numerical methods for ordinary differential equations |
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
| 34K28 | Numerical approximation of solutions of functional-differential equations (MSC2010) |
