Help solving 3 ODEs
1 view (last 30 days)
Show older comments
I'm trying to solve these 3 ODEs with ODE45.
d(xA)/d(v)=(0.2*(0.6^2)*((1-(0.375*xA)))*(((5/3)-xA)/(1-0.375*xA))))/(3); d(xB)/d(v)=(0.2*(0.6^2)*((1-xB)/(1-(0*xB)))*(((5/3)-xB)/(1-0*xB)))/(3); d(xC)/d(v)=(0.2*(0.6^2)*((1-xC)/(1-(0.75*xC)))*(((5/3)-xC)/(1-0.75*xC)))/(3); v(f)=47 v(0)=0 xA(0)=0 xB(0)=0 xC(0)=0
What do I do?
0 Comments
Accepted Answer
Stephan
on 22 Oct 2018
Edited: Stephan
on 22 Oct 2018
Hi,
try this:
syms xA(v) xB(v) xC(v)
eqn1 = diff(xA, v) == (0.2*(0.6^2)*((1-(0.375*xA)))*(((5/3)-xA)/(1-0.375*xA)))/(3);
eqn2 = diff(xB, v) == (0.2*(0.6^2)*((1-xB)/(1-(0*xB)))*(((5/3)-xB)/(1-0*xB)))/(3);
eqn3 = diff(xC, v) == (0.2*(0.6^2)*((1-xC)/(1-(0.75*xC)))*(((5/3)-xC)/(1-0.75*xC)))/(3);
[odes, vars] = odeToVectorField(eqn1, eqn2, eqn3);
fun = matlabFunction(odes,'Vars',{'t','Y'});
x0 = [0 0 0];
tspan = [0 47];
[t, sol] = ode45(fun,tspan,x0);
xA = sol(:,2);
xB = sol(:,1);
xC = sol(:,3);
plot(t,xA,t,xB,t,xC)
legend('xA','xB','xC','Location','southeast')
Note that for some reasons Matlab changes the order of the variables, so that xA = Y(2) and xB = Y(1):
odes =
((Y[1] - 5/3)*((9*Y[1])/125 - 9/125))/3
-((Y[2] - 5/3)*((27*Y[2])/1000 - 9/125))/(3*((3*Y[2])/8 - 1))
(3*(Y[3] - 1)*(Y[3] - 5/3))/(125*((3*Y[3])/4 - 1)^2)
vars =
xB
xA
xC
- dont ask me why this happens, but you have to take it into account. The result is:
.
Best regards
Stephan
More Answers (0)
See Also
Categories
Find more on Ordinary Differential Equations in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!