Solving six differential equations with ODE 45 solver without defining y terms? Matlab

Question

I am trying to solve differential equations by using ode45 solver. However, it does not work as expected.

function ydot=Untitledrt(z,y)
    ydot = zeros(6,1);
    %y(1)=A
    %y(2)=B
    %y(3)=C
    %y(4)=D
    %y(5)=P
    %y(6)=T
    m1 = 6;
    m2 = 9;
    m3 = 5;
    k1 = 6;
    k2 = 7;
    k3 = 4;
    k4 = 1;
    c1 = 1;
    c2 = 0.2;
    c3 = 0.1;
    c4 = 2;
    F1 = 3;
    F2 = 9;
    F3 = 12;
    ydot(1)=y(2)
    ydot(2)=((-((k1+k2)./m1)).*y(1))-(((c1+c2)./m1).*y(2))+((k2./m1).*y(3))+ ((c2./m1).*y(4))+(F1./m1)
    ydot(3)=y(4)
    ydot(4)=((k2./m2).*y(1))+((c2./m2).*y(2))-(((k2+k3)./m2).*y(3))-(((c2+c3).*m2).*y(4))+((k3/m2).*y(5))+((c3./m2).*y(6))+(F2./m2)
    ydot(5)=y(6)
    ydot(6)=((k2./m3).*y(3))+((c3./m3).*y(4))-(((k3+k4)./m3).*y(5))-(((c3+c4)./m3).*y(6))+(F3./m3)

MATLAB keeps returning the following error message:

Not enough input arguments.

Error in Untitledrt (line 24)

ydot(1)=y(2)

I understand that the error is due to not defining the y terms. Some other examples of ODE45 solver codes also do not define y terms. Is there something I am missing? Or someone can please suggest something to make this code work without defining y terms. Thank you in advance.

How are you calling ODE45? Your function y must be a vector — Mikhail Genkin
Also note that z here would be the t of the ODE, which you're not using (meaning your system is autonomous). In this case you should be able to replace it with ~, i.e. function ydot=Untitledrt(~,y), which in many cases MATLAB will recognise and help speed up the code by not instantiating that variable when making the call. Might not be an an issue here, but a good habit to develop. — Steve Heim

zhk zhk · Accepted Answer · 2016-12-02T05:04:36

First create an M-file which evaluates the right-hand side of the system f(t,y) for any given t, y1, y2, y3, y4, y5, y6 and name it as you Untitledrt.m.

function ydot=Untitledrt(t,y)
ydot = zeros(6,1);
m1 = 6;
m2 = 9;
m3 = 5;
k1 = 6;
k2 = 7;
k3 = 4;
k4 = 1;
c1 = 1;
c2 = 0.2;
c3 = 0.1;
c4 = 2;
F1 = 3;
F2 = 9;
F3 = 12;
ydot(1)=y(2)
ydot(2)=((-((k1+k2)./m1)).*y(1))-(((c1+c2)./m1).*y(2))+((k2./m1).*y(3))+ ((c2./m1).*y(4))+(F1./m1)
ydot(3)=y(4)
ydot(4)=((k2./m2).*y(1))+((c2./m2).*y(2))-(((k2+k3)./m2).*y(3))-(((c2+c3).*m2).*y(4))+((k3/m2).*y(5))+((c3./m2).*y(6))+(F2./m2)
ydot(5)=y(6)
ydot(6)=((k2./m3).*y(3))+((c3./m3).*y(4))-(((k3+k4)./m3).*y(5))-(((c3+c4)./m3).*y(6))+(F3./m3)

Now type in the following commands in MatLab window line by line or paste it in a new script file

[t,Y]=ode45('Untitledrt',[0 10],[1;-1;0;0;0;0]); 

plot(t,Y(:,1),'+',t,Y(:,2),'x',t,Y(:,3),'o',t,Y(:,4),'o',t,Y(:,5),'o',t,Y(:,6),'o')

Plot of the six dependent variables

Solving six differential equations with ODE 45 solver without defining y terms? Matlab

1 Answers