Determine where lines intersect

Hey! Im wondering how i could Determinate the intersect of these two lines. I got the following code.

    z0=10000;
dz0=0;
span=[0 250];
[T,Y] = ode45(@function_A,span,[z0 dz0]);
x=linspace(0,300,2000);
plot(T,Y(:,1),'b', x,0,'g');

and this function

   function dz = function_A(t,z)
dz = zeros(2,1);
g=9.81;
m=250;
lambda=7.5*10^3;
k0=(m*g)/((250/3.6)^2);
k=@(z)k0.*exp(-z./lambda);
dz(1)=z(2);
dz(2)=-g-(k(z(1)).*abs(z(2))*z(2))/m;
end

Anyone who can help me?

Answer 1

[Mischa Kim]

Hello Andreas, use ode events. This examples shows how to detect events with the bouncing ball problem. Check out the following:

 function my_ode()
 z0  = 10000;
 dz0 = 0;
 span=[0 250];
 options = odeset('Events',@events);
 [T,Y,Te,Ye,Ie] = ode45(@function_A,span,[z0 dz0],options);
 x = linspace(0,300,2000);
 plot(T,Y(:,1),'b', x,0,'g');
 end

 function dz = function_A(t,z)
 dz     = zeros(2,1);
 g      = 9.81;
 m      = 250;
 lambda = 7.5*10^3;
 k0     = (m*g)/((250/3.6)^2);
 k      = @(z)k0.*exp(-z./lambda);
 dz(1)  = z(2);
 dz(2)  = -g-(k(z(1)).*abs(z(2))*z(2))/m;
 end

 function [value,isterminal,direction] = events(t,y)
 % Locate the time when height passes through zero in a 
 % decreasing direction and stop integration.
 value      = y(1);     % Detect height = 0
 isterminal = 1;        % Stop the integration
 direction  = 0;        % Negative direction only
 end

[Jan]

The function to be integrated contains an abs() . This is a non-smooth function and inconsequence the solution suffers from the problems described here. The step size control of ODE45 must fail at the changes of the sign. To handle this, the step size is reduced until the discontinuity is covered by the rounding errors.

Better use an event function and restart the integration at the discontinuity.