Application of A-stable bilateral approximation to the integration of ordinary differential equations (Q1074316)

The aim of this paper, which is closely related with a previous paper of the second author and \textit{G. Gheri} [Calcolo 19, 301-320 (1982; Zbl 0511.65052)], is to establish the conditions that must be satisfied by a differential equation in order to obtain bilateral approximations to the solutions by means of A-stable numerical methods. In particular the authors consider one-step predictor corrector methods where the corrector is a 0-method and the predictor is a semi-explicit method derived from the corresponding corrector. It is shown that if these methods are applied to differential equations with some monotony conditions it is possible to compute bilateral approximations to its solutions. Finally some numerical examples that confirm the theoretical results are presented.