Solving a coupled system of ODE's that depend on different variables

I have a set of coupled ODE's that I need to solve. However, the ODE's are not dependent on the same variable. For example I have the following first order system:

dA0/dx = A, 
dA/dx = f(A0(x), A(x), F(y), y)  
dF/dy = f(A0(x), A(x), y).

For example, the dF/dy looks like: p*(y-y^2)*(A0*A+A^2) where p is a constant And the dA/dx equation looks like: ([p*A0*(y-y^2)-A0]*A)/(F+A*(y-y^2))

The first dA0/dx is to get them all down to first order.

Is there a numerical or analytic method to solve these since the derivatives are dependent on different variables? All the solutions I can find need dA and dF to be with respect to the same variable and I can't get ODE45 to work with these equations.

Here is my current code:

dx=(L/H)/100; x=(0:dx:(L/H))'; y=[0:H/(size(x,1)-1):H]; %Pressure drop through Unexposed area %Pressure drop count=1; % Equation: A3 = (420/(11*Re0))+(g(i)*h(i)+84/11*f(i)*g(i)-35/11*NClam/Re0*h(i)-70/11*Cturb*g(i)*h(i)-70/11*1/Re0*h(i))/f(i); while count <2 f=zeros(length(x),1); % f=A g=zeros(length(x),1); % g=A' h=zeros(length(x),1); % h=A'' A3=zeros(length(x),1); % A3=A''' f(1)=-.99; %Boundary Condition at dead end g(1)=0; %Boundary Condition at dead end %1st 2 Shooting Guesses SG(1)=.0001; SG(2)=.00012;

    for j=1:2
    h(1)=SG(j);
        for i=1:size(x,1)-1
            % Runge Kutta Slopes
            k1f=dx*g(i);
            k1g=dx*h(i);
            k1h=dx*((420/(11*Re0))+(g(i)*h(i)+84/11*(1+f(i))*g(i)-35/11*NClam/Re0*h(i)-70/11*Cturb*g(i)*h(i)-70/11*1/Re0*h(i))/(1+f(i)));
            k2f=dx*(g(i)+1/2*k1g);
            k2g=dx*(h(i)+1/2*k1h);
            k2h=dx*((420/(11*Re0))+((g(i)+1/2*k1g)*(h(i)+1/2*k1h)+84/11*(1+(f(i)+1/2*k1f))*(g(i)+1/2*k1g)-35/11*NClam/Re0*(h(i)+1/2*k1h)-70/11*Cturb*(g(i)+1/2*k1g)*(h(i)+1/2*k1h)-70/11*1/Re0*(h(i)+1/2*k1h))/(1+(f(i)+1/2*k1f)));
            k3f=dx*(g(i)+1/2*k2g);
            k3g=dx*(h(i)+1/2*k2h);
            k3h=dx*((420/(11*Re0))+((g(i)+1/2*k2g)*(h(i)+1/2*k2h)+84/11*(1+(f(i)+1/2*k2f))*(g(i)+1/2*k2g)-35/11*NClam/Re0*(h(i)+1/2*k2h)-70/11*Cturb*(g(i)+1/2*k2g)*(h(i)+1/2*k2h)-70/11*1/Re0*(h(i)+1/2*k2h))/(1+(f(i)+1/2*k2f)));
            k4f=dx*(g(i)+k3g);
            k4g=dx*(h(i)+k3h);
            k4h=dx*((420/(11*Re0))+((g(i)+k3g)*(h(i)+k3h)+84/11*(1+(f(i)+k3f))*(g(i)+k3g)-35/11*NClam/Re0*(h(i)+k3h)-70/11*Cturb*(g(i)+k3g)*(h(i)+k3h)-70/11*1/Re0*(h(i)+k3h))/(1+(f(i)+k3f)));

            % Evaluation
            f(i+1)=f(i)+1/6*(k1f+2*k2f+2*k3f+k4f);
            g(i+1)=g(i)+1/6*(k1g+2*k2g+2*k3g+k4g);
            h(i+1)=h(i)+1/6*(k1h+2*k2h+2*k3h+k4h);
        end
        % R is f at channel end, we want equal to Uout
        R(j)=f(size(x,1));
        err=abs(uout-(R(j)));
    end

    % This loop iterates to find the right guess for f''(0) so that
    % f(x/L)= Uout

    while err>1e-9
        j=j+1;
            % New guess is found by linear interposation of the last 2 guesses
        SG(j)=SG(j-2)+(SG(j-1)-SG(j-2))/(R(j-1)-R(j-2))*(-R(j-2));
        h(1)=SG(j);
        for i=1:size(x,1)-1
            % Runge Kutta Slopes
            k1f=dx*g(i);
            k1g=dx*h(i);
            k1h=dx*((420/(11*Re0))+(g(i)*h(i)+84/11*(1+f(i))*g(i)-35/11*NClam/Re0*h(i)-70/11*Cturb*g(i)*h(i)-70/11*1/Re0*h(i))/(1+f(i)));
            k2f=dx*(g(i)+1/2*k1g);
            k2g=dx*(h(i)+1/2*k1h);
            k2h=dx*((420/(11*Re0))+((g(i)+1/2*k1g)*(h(i)+1/2*k1h)+84/11*(1+(f(i)+1/2*k1f))*(g(i)+1/2*k1g)-35/11*NClam/Re0*(h(i)+1/2*k1h)-70/11*Cturb*(g(i)+1/2*k1g)*(h(i)+1/2*k1h)-70/11*1/Re0*(h(i)+1/2*k1h))/(1+(f(i)+1/2*k1f)));
            k3f=dx*(g(i)+1/2*k2g);
            k3g=dx*(h(i)+1/2*k2h);
            k3h=dx*((420/(11*Re0))+((g(i)+1/2*k2g)*(h(i)+1/2*k2h)+84/11*(1+(f(i)+1/2*k2f))*(g(i)+1/2*k2g)-35/11*NClam/Re0*(h(i)+1/2*k2h)-70/11*Cturb*(g(i)+1/2*k2g)*(h(i)+1/2*k2h)-70/11*1/Re0*(h(i)+1/2*k2h))/(1+(f(i)+1/2*k2f)));
            k4f=dx*(g(i)+k3g);
            k4g=dx*(h(i)+k3h);
            k4h=dx*((420/(11*Re0))+((g(i)+k3g)*(h(i)+k3h)+84/11*(1+(f(i)+k3f))*(g(i)+k3g)-35/11*NClam/Re0*(h(i)+k3h)-70/11*Cturb*(g(i)+k3g)*(h(i)+k3h)-70/11*1/Re0*(h(i)+k3h))/(1+(f(i)+k3f)));

            % Evaluation
            f(i+1)=f(i)+1/6*(k1f+2*k2f+2*k3f+k4f);
            g(i+1)=g(i)+1/6*(k1g+2*k2g+2*k3g+k4g);
            h(i+1)=h(i)+1/6*(k1h+2*k2h+2*k3h+k4h);
        end
        % R is f at channel end, we want equal to Uout
        R(j)=f(size(x,1));
        err=abs(uout-(R(j)));
    end

    % Calculate A'''
    for i = 1:length(x)
    A3(i) = (420/(11*Re0))+(g(i)*h(i)+84/11*(1+f(i))*g(i)-35/11*NClam/Re0*h(i)-70/11*Cturb*g(i)*h(i)-70/11*1/Re0*h(i))/(1+f(i));
    end

    % Calculate U and V
    for n = 1:length(x)
        for m = 1:length(y)
            U(n,m) = uout.*(1+f(n)).*(6*(y(m)/H).*(1-(y(m)/H)));
            V(n,m) = -uout.*g(n)*(3*(y(m)/H).^2-2*(y(m)/H).^3); 
        end
    end
    count = count+1;
end

[Sara]

What does not work in ode45? try posting your code, including the inputs.

[ragesh r menon]

I use ode45 to solve coupled nonlinear ODEs and get accurate results. For example my state equations are

   function dxdt=LOS(t,x)
  ......
    dxdt(1)=Vs*cos(x(5)-x(2))-Vt*cos(x(7)-x(2));%LOS separation
     dxdt(2)=(Vs*sin(x(5)-x(2))-Vt*sin(x(7)-x(2)))/x(1);%sLOS rate
    ......
  end

[Sara]

But what error did you get? Post the whole code