Differential equation ode45 matlab

Hi! I have a differential equation and I try to solve them by Matlab (ODE45) For example:

     function dy = f8(t,y)
      dy = 3 - 3./25.*y;   %(1)

     tspan = [0, 2]; y0 = -3;
     [Y,T] = ode45(@f8, tspan, y0);
     plot(Y,T)
     grid on

When the curve reaches=0, I have to go to the equation of (2):

     dy = 10-3./10.*y;  %(2)

Please, help me, How can I do it?

Answer 1

[Star Strider]

You need to detect the zero-crossing as an ‘event’. See the documentation on Event Location for details.

It is not difficult, but it can be a bit of a challenge to get it working the first time you do it.

[Alex7210]

Thanks for your answer! I could detect zero-crossing.

      tspan = [0, 10]; x0 = -3;
      options = odeset('Events', @kg15);
      [t,x,te,xe,ie] = ode45(@f8, tspan, x0, options);
       plot(t,x); grid on
%==============================

      function dy = f8(t,y)
      dy = 3-3./25.*y;
%==============================

      function [value, isterminal, ...
      direction] = kg15(t,x)

      value = x-0;
      isterminal = 1;
      direction = 1;

But how can I continue my second equation? Help me please to understand it

[Star Strider]

First, when the integration stops at the zero-crossing, immediately store your first set of t and x values as an array so they do not get overwritten.

Second, use the last t and x values for your new initial t and x values, call ode45 with your second function and those initial conditions and time, and continue integrating until the end of tspan.

Third, append your second set of t and x values to your first set to get the complete integration sequence. (It does not appear from your second ODE that you will have another zero-crossing, so you will only have to do this once.)