@Carl Love

Thank you Carl, I was thinking about the same. But this does not work. In the events-help is explained that    pre(x(t)) works ONLY in the conditions for the conditional events. I really do not understand why. Is it so complicated to permit the user to get  the previous value in dsolve for any purposes, if maple can somehow  use this value already ? Really strange.

@Carl Love 

Thank you Carl Love. This was the first simple solution, I was trying. But the further sucsess  depends on the form of the derivative. For example, if it has the form sin(x)*exp(-x), this criterium for stopping the calculations stops at quite random places, depending on the current  value of the  sin(x). Hence, the better criterium can be obtained by averaging the result on several successive points.  Unfortunately, I do not know how to get them from maple dsolve precedure.

Thank you Kitonum 1595,

Your idea is correct and really works and I will try to use it in the my real problem. I'm afraid, it will work quite slowly for more complicated systems of ODE, since increasing “a” by “h” one can start the calculation  from the very beginning. If one has access to the very real Maple code, one will be able to remember the last but one value of calculation and then to use the proper stop-condition. The real problem is how to do this using the permitted Maple tools.

Plamen

Thank you Kitonum 1595,

Your idea is correct and really works and I will try to use it in the my real problem. I'm afraid, it will work quite slowly for more complicated systems of ODE, since increasing “a” by “h” one can start the calculation  from the very beginning. If one has access to the very real Maple code, one will be able to remember the last but one value of calculation and then to use the proper stop-condition. The real problem is how to do this using the permitted Maple tools.

Plamen