ODE45 stop after all events have fired

I have a code in which I'm integrating the motion of several particles. I want the integration to terminate when all of the particles have had at least one crossing point in their velocity. So I tried an event code that looks like

function [val, isterm, dir] = event(t,y)
global stopped;

val = y(length(y)/2+1:end);
stopped(val==0)=1;
val = [val; all(stopped)];

isterm = 0*val; isterm(end)=1;
dir = 0*val;

But the line

    stopped(val==0)=1

doesn't indicate when an event happened, because events is looking for a zero crossing. So, how can I tell (inside the event function) that the event is going to fire? Or is there an easier way to do this?

Answer 1

[Teja Muppirala]

One way of doing this would be to call the ODE solver repeatedly in a loop, until you find that all particles have set off events. Each iteration will start off at the previous time and state. This has 3 particles moving with different velocities, and integrates until they all cross zero.

function my_ode_fun
global elist
options = odeset('Events',@event_function);

   elist = zeros(1,3);
   tstart = 0;
   tend = 100;
   ystart = [1;2;3];
   t_all = [];
   y_all = [];

   figure;
   hold on;
    while ~all(elist)
      [tout,yout,te,ye,enum] = ode45(@(t,x) [-1;-.25;-.5], [tstart tend],ystart,options);
      elist(enum(end)) = 1;
       ystart = ye(end,:);
       tstart = te(end,:);
       t_all = [t_all; tout];
       y_all = [y_all; yout];
       plot(tstart*[1 1], [-5 5],'k');
   end
   plot(t_all, y_all);
   grid on;

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

global elist
value = [x(1) x(2) x(3)];  % when value = 0, an event is triggered
isterminal = ~elist; 
direction = [0 0 0];

[Eoin]

Yes, this would work, but isn't as elegant/efficient as I was hoping for..

I finally settled for running the particles in their own ode45 calls, but this only works because the particles are actually non-interacting.

[Jan]

@Eoin: When it works, the correct result is a good compensation for a lack of elegance.