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**Recent progress in extrapolation methods for ordinary differential equations.**
*(English)*
Zbl 0602.65047

The first extrapolation method for ordinary differential equations was suggested by Richardson already in 1910. However such methods became competitive to the established methods of Adams and Runge-Kutta type only in the sixties. More precisely successful extrapolation methods were developed until very recently only for nonstiff differential equations. The author is the initiator of integrators suitable for the stiff case too.

This paper is a survey on the state-of-art in the field of extrapolation methods for the Cauchy problem for ordinary differential equations. It includes extensive numerical work, which enables a comparison and evaluation of existing classical and extrapolation methods. Several lines for possibly future research work are also sketched. A reference list of 54 papers concludes the article.

This paper is a survey on the state-of-art in the field of extrapolation methods for the Cauchy problem for ordinary differential equations. It includes extensive numerical work, which enables a comparison and evaluation of existing classical and extrapolation methods. Several lines for possibly future research work are also sketched. A reference list of 54 papers concludes the article.

Reviewer: E.Schechter

### MSC:

65L05 | Numerical methods for initial value problems involving ordinary differential equations |

34A34 | Nonlinear ordinary differential equations and systems |