The Open Mathematics Journal

2013, 6 : 19-25
Published online 2013 November 8. DOI: 10.2174/1874117701306010019
Publisher ID: TOMATJ-6-19

T-Stability of General One-Step Methods for Abstract Initial-Value Problems

Istvan Farago and Imre Fekete
Department of Applied Analysis and Computational Mathematics, Eötvös Lorand, University, Pazmany P. s. 1/C, 1117, Budapest, Hungary.

ABSTRACT

In this paper we investigate the T-stability of one-step methods for initial-value problems. The main result is that we extend the classical result (the well-known Euler method) for variable step size explicit and implicit one-step methods. In addition, we give further properties for the theory of T-stability of nonlinear equations in an abstract (Banach space) setting.

Keywords:

Finite difference method, stability, convergence.