Coupled ODE with ode45

Hello, I am trying to solve these two coupled differential equations, but I can't seem to get it to work. I always have difficulty using ODE45...but why isn't the variable X being recognized? The image shows the differential equations I am trying to solve using MATLAB

alpha = 0.001; % L^-1
FA0 = 2.5; % mol/min
CA0 = 0.305; % mol/L
eps = 2;
k = 0.044;

CA = @(y,X) CA0*(1-X).*y./(1+eps*X);
rA = @(y,X) -k*CA(y,X);

vSpan = [0 500]; % L
dXdV = @(V,X) -rA(y,X)/FA0;
dydV = @(V,y) -alpha*(1+eps.*X)./(2*y);

[V, Y] = ode45(dydV,vSpan,1);
[V, X] = ode45(dXdV,vSpan,0);

But this is the error I encounter

Undefined function or variable 'X'.

Error in @(V,y)-alpha*(1+eps.*X)./(2*y)

Error in odearguments (line 88)
f0 = feval(ode,t0,y0,args{:});   % ODE15I sets args{1} to yp0.

Error in ode45 (line 114)
[neq, tspan, ntspan, next, t0, tfinal, tdir, y0, f0, odeArgs, odeFcn,
...

Answer 1

[Zoltán Csáti]

I found the mistake. It was a sign. :) The correct function is

function dz = myode(v,z)

alpha = 0.001;
C0 = 0.3;
esp = 2;
k = 0.044;
f0 = 2.5;
dz = zeros(2,1);
dz(1) = k*C0/f0*(1-z(1)).*z(2)./(1+esp*z(1));
dz(2) = -alpha*(1+esp*z(1))./(2*z(2));

[Rick]

so when doing coupled ODE's, then you want the variables in the same array, instead of trying to have two separate ode45 calls like I was doing at first? Where was I going wrong in my method?

[Zoltán Csáti]

In general, a coupled differential equation system can not be decoupled. So yes, all the dependent variables are put into a vector. Your method was wrong because you could not decouple the equations.

[Rick]

Thank you!

[faiz islam]

@Zoltan ,i tried it but where is "z" defined?i got error.can you share full code?

faiz

[santosh kumar]

to define a function, use "syms function" example: to define x y z syntax: "syms x y z"

Answer 2

[Zoltán Csáti]

On line dydV = @(V,y) -alpha*(1+eps.*X)./(2*y); X is not included. I would solve it as a coupled system or solve it analytically by hand. I don't see the impact of C in the differential equations. Is C needed?

[Rick]

the Concentration (CA) is needed for rA, which is in the dXdV differential equation

Answer 3

[Zoltán Csáti]

Code your function as follows.

function dz = myode(v,z)

alpha = 0.001;
C0 = 0.3;
esp = 2;
k = 0.044;
f0 = 2.5;
dz = zeros(2,1);
dz(1) = k*C0/f0*(1-z(1)).*z(2)./(1-esp*z(1));
dz(2) = -alpha*(1+esp*z(1))./(2*z(2));

Then call it as

[v z] = ode45(@myode,[0 500],[0 1]);

[Rick]

use plot(v,z) and you will see what the heck is going on with one of the functions. It is oscillating like crazy

[Zoltán Csáti]

Yes, I plotted it. It is very sensitive to the parameters. Try different parameter values.