A symbolic-numerical method to integrate ODEs at a singular point

Classical numerical codes are not valid for the integration of singular ini tial Value problems. However, these problems are very common in the applied sciences. An example is the study of the elastic equations of the earth in cluding the effect of the solid inner core. Frequently, the technique used is the introduction of a change of variable (mainly blowing-up) that remove the singularity or reduce the singularity to an other more simple. In this paper, we propose the combination of a symbolic technique, which let us ob tain parameterizations of the solutions in the singular point, with a class ical numerical code that we initialize with the symbolic solution. There ar e a lot of extensions of these techniques. Here we only present a first app roach to the problem. (C) 1999 Elsevier Science Ltd. All rights reserved.