Portal de Periódicos da CAPES

Runge–Kutta Solutions of Stiff Differential Equations Near Stationary Points

1995; Society for Industrial and Applied Mathematics; Volume: 32; Issue: 4 Linguagem: Inglês

10.1137/0732060

1095-7170

Ch. Lubich, Kaspar Nipp, D. Stoffer,

Advanced Mathematical Modeling in Engineering

Runge–Kutta methods applied to stiff systems in singular perturbation form are shown to give accurate approximations of phase portraits near hyperbolic stationary points. Over arbitrarily long time intervals, Runge–Kutta solutions shadow solutions of the differential equation and vice versa. Precise error bounds are derived. The proof uses attractive invariant manifolds to reduce the problem to the nonstiff case, which was previously studied by Beyn.