Extrapolation at stiff differential equations. (English) Zbl 0643.65034

Hairer, E.; Lubich, C.

Numer. Math. 52, No. 4, 377-400 (1988).

Asymptotic expansions for the global error for extrapolation methods using the implicit Euler method, the linearly implicit Euler method and the linearly implicit midpoint rule for stiff initial value problems in ordinary differential equations are derived. Practical implications of these results for error estimation and step-size control are indicated. Numerical examples are given.

Reviewer: S.Filippi

MSC:

65L05	Numerical methods for initial value problems involving ordinary differential equations
34A34	Nonlinear ordinary differential equations and systems

Keywords:

Asymptotic expansions; global error; extrapolation methods; implicit Euler method; implicit midpoint rule; stiff initial value problems; error estimation; step-size control; Numerical examples

Software:

DEPAC

References:

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