Solve a second order differential equation with ODE45

1 view (last 30 days)
Hello,
I had managed to make this file work but recently it's very slow and I'm not able to run it properly. I think the issue might come form the vectors. Here is the script and function file:
function xdot = OWC (t,x)
global g h a
xdot = [((g*h-((x(2).^2)/2)-g*x(1))/(x(1)+a)); x(1)];
and the script:
global g h a;
g=9.81;
h=0;
for a=0;
[t,x] = ode45('OWC',[0 10],[1.0 1.0]);
plot (t,x)
hold on
end
for a=1;
[t,x] = ode45('OWC',[0 10],[1.0 1.0]);
plot (t,x)
hold on
end
The original equation is: y"=(g*h-(y'^2/2)-g*z)/(z+a)
I haven't used Matlab much so I wouldn't be surprised if I'm using the wrong technique but I did manage to make this script work before and somehow I've ruined it.
Thank you.
  1 Comment
Peter Grant
Peter Grant on 24 Jan 2014
Whenever I change the y0 in
[t,x] = ode45('OWC',[0 10],[1.0 1.0]);
From [1.0 1.0] to [0 0], the script finishes but without giving an answer. That's why I think the slow process of the script might be because of these initial conditions.

Sign in to comment.

Accepted Answer

Mischa Kim
Mischa Kim on 25 Jan 2014
Hello Peter, there are a couple of issues:
  • It looks like you want to use if rather than for statements to execute either of the blocks depending on the value of a , correct?
  • When you set the initial conditions to [0; 0] and with h = 0 the derivatives are all zero at all time so you get a flat line (provided that a != 0).
  • When you set the initial conditions to [0; 0] and with a = 0, h = 0 you have a devide by zero the differential equations resulting in NaN.
  1 Comment
Peter Grant
Peter Grant on 25 Jan 2014
Thank you! This really helped, I had realized that by changing 'h' my script seemed to run better but I didn't really try to figure out why. It was stupid of me not to look into the mathematical aspect of the script rather than technical aspect.

Sign in to comment.

More Answers (0)

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!