How can I solve a differential equation on non-fixed interval?

I am trying to solve a first order ODE with such conditions: y(0) = 0, y(x_0)=1,

where x_0 must be determined with the last condition. Therefore I have to be solving the ODE until y=1. But MATLAB requires setting of all integration interval before solving.

The trivial way is to change the interval on fixed step each time when y does not achieve 1 and to solve the equation again. But this method takes a lot of time for calculations.

Is there any different way to solve a ODE on non-fixed interval?

Answer 1

[Torsten]

Use the "Event"-facility of the ODE-integrators and stop integraton if y=1.

Example under

https://www.mathworks.com/examples/matlab/mw/matlab-ex84325677-simple-event-location-a-bouncing-ball

Best wishes

Torsten.

[Ilya Kalash]

Thanks, Torsten. I've made this.

Also here is detail explanation https://www.mathworks.com/help/matlab/math/ode-event-location.html