Runge-Kutta solutions of stiff differential equations near stationary points

Autor:	Lubich, Christian, Nipp, Kaspar, Stoffer, D.
Jazyk:	angličtina
Rok vydání:	1993
Předmět:	Long-time error bounds implicit Runge-Kutta method FOS: Mathematics invariant manifold shadowing singular perturbation problem ddc:510 hyperbolic equilibrium stiff ODE Mathematics
Zdroj:	SAM Research Report, 1993-01
DOI:	10.3929/ethz-a-004283920
Popis:	Runge-Kutta methods applied to stiff systems in singular perturbation form are shown to give accurate approximations of phase portraits near hyperbolic stationary points. We prove that Runge-Kutta solutions shadow solutions of the differential equation over arbitrarily long time intervals, and vice versa. Sharp error estimates are derived. The proof uses attractive invariant manifolds to reduce the problem to the nonstiff case which was previously studied by Beyn. SAM Research Report, 1993-01
Databáze:	OpenAIRE
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