We investigate stability properties of two-step Runge-Kutta methods with respect to the linear test equation y′(t) = ay(t) + by (t - ρ), t ≥ 0, y(t) = g(t), t ∈ [-ρ,0], where a and b are complex parameters. It is known that the solution y(t) to this equation tends to zero at t → ∞ if |b| < - Re(a). We will show that under some conditions this property is inherited by any A-stable two-step Runge-Kutta method applied on a constrained mesh to delay differential equations, i.e., that the corresponding method is P-stable.
ASJC Scopus subject areas
- Modeling and Simulation
- Computational Theory and Mathematics
- Computational Mathematics