## Abstract

The one-step implicit methods, the backward Euler being the most known, require the solution of a nonlinear equation at each step.To avoid this, these methods can be approximated by making use of a one step of a Newton method. Thus the methods are transformed into some explicit ones. We will obtain these transformed methods, find conditions under which they generate continuous dynamical systems and show their order of convergence. Some results on the stability of these explicit schemes, as well as on the shadowing phenomenon are also carried out. Concluding remarks and some open problems end the paper.

## Authors

Călin-Ioan** Gheorghiu
**Tiberiu Popoviciu Institute of Numerical Analysis

## Keywords

## Paper coordinates

C.I. Gheorghiu, *On some one-step implicit methods as dynamical systems*, Rev. Anal. Numér. Théor. Approx., **32** (2003) 171-175.

## About this paper

##### Journal

Rev. Anal. Numér. Théor. Approx

##### Publisher Name

Editura Academiei Romane

##### Paper on the journal website

##### Print ISSN

1222-9024

##### Online ISSN

##### MR

?

##### ZBL

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