@article{Gheorghiu_2003, title={On some one-step implicit methods as dynamical systems}, volume={32}, url={https://ictp.acad.ro/jnaat/journal/article/view/2003-vol32-no2-art5}, DOI={10.33993/jnaat322-745}, abstractNote={<pre>The one-step implicit methods, the backward Euler being the most</pre><pre> known, require the solution of a nonlinear equation at each step.</pre><pre>To avoid this, these methods can be approximated by making use of</pre><pre> a one step of a Newton method. Thus the methods are transformed</pre><pre> into some explicit ones. We will obtain these transformed methods,</pre><pre> find conditions under which they generate continuous dynamical</pre><pre> systems and show their order of convergence. Some results on the</pre><pre> stability of these explicit schemes, as well as on the shadowing</pre><pre> phenomenon are also carried out. Concluding remarks and some open problems end the paper.</pre>}, number={2}, journal={Rev. Anal. Numér. Théor. Approx.}, author={Gheorghiu, Călin-Ioan}, year={2003}, month={Aug.}, pages={171–175} }