Solving differential equation with varying Constant

Dimensions

G= 1x100, H=1X100;

I want to solve these 7 eqns. I am using ODE45. I am able to solve these equations for fixed T and Q. But i want to solve it for varying T and Q. Thats why i am using for loop. Can some one explain where am I wrong?. I have tried myself but unable to figure it out.

function [dUdt]=eqn(t,U)
 dUdt=zeros(7,1);
 K=0.003;
for i=1:100
    T=G(1,i);
    Q=H(1,i);
   
end
 
 dUdt(1)=2*K*T(i)*(U(2)-U(1));
 dUdt(2)=-2*K*U(2)*T(i);
 dUdt(3)=K*T(i)*(2*Q(i)-U(3))-U(3)*K*(U(1)+2*U(2));
 dUdt(4)=K*U(3)*T(i)-U(4)*K*(U(1)+2*U(2));
 dUdt(5)=K*Q(i)*(U(1)+2*U(2))-2*K*U(5)*T(i);
 dUdt(6)=K*U(3)*(U(1)+2*U(2))+2*K*U(5)*T(i)-K*U(6)*T(i);
 dUdt(7)=K*U(6)*T(i)+U(4)*K*(U(1)+2*U(2)); 
 
end

Answer 1

[Torsten]

function [dUdt]=eqn(t,U)

 dUdt=zeros(7,1);

 K=0.003;
 t_inter=0:99;
 T_actual=interp1(t_inter,G,t);
 Q_actual=interp1(t_inter,H,t);

 dUdt(1)=2*K*T_actual*(U(2)-U(1));
 dUdt(2)=-2*K*U(2)*T_actual;
 dUdt(3)=K*T_actual*(2*Q_actual-U(3))-U(3)*K*(U(1)+2*U(2));
 dUdt(4)=K*U(3)*T_actual-U(4)*K*(U(1)+2*U(2));
 dUdt(5)=K*Q_actual*(U(1)+2*U(2))-2*K*U(5)*T_actual;
 dUdt(6)=K*U(3)*(U(1)+2*U(2))+2*K*U(5)*T_actual-K*U(6)*T_actual;
 dUdt(7)=K*U(6)*T_actual+U(4)*K*(U(1)+2*U(2)); 

 end

[P K]

Getting this error.Undefined function or variable 'G'.

Error in eqn (line 5)

T_actual=interp1(t_inter,G,t);

G is visible in workspace.

[Torsten]

If you can use G in your file, I see no reason why you shouldn't be able to use it in the modified file.

[P K]

I don't know why is it happening.

[madhan ravi]

+1 works perfectly!

[P K]

+1 works perfectly!

I didn't understood @madhan

[madhan ravi]

tspan=[...];
initial_conditions=[...];
[t,x]=ode45(@eqn,tspan,initial_conditions);
plot(t,x(:,1)) % to plot the solutions

function [dUdt]=eqn(t,U)
 G=....your values;
 H=....your values;
 dUdt=zeros(7,1);
 K=0.003;
 t_inter=0:99;
 T_actual=interp1(t_inter,G,t);
 Q_actual=interp1(t_inter,H,t);
 dUdt(1)=2*K*T_actual*(U(2)-U(1));
 dUdt(2)=-2*K*U(2)*T_actual;
 dUdt(3)=K*T_actual*(2*Q_actual-U(3))-U(3)*K*(U(1)+2*U(2));
 dUdt(4)=K*U(3)*T_actual-U(4)*K*(U(1)+2*U(2));
 dUdt(5)=K*Q_actual*(U(1)+2*U(2))-2*K*U(5)*T_actual;
 dUdt(6)=K*U(3)*(U(1)+2*U(2))+2*K*U(5)*T_actual-K*U(6)*T_actual;
 dUdt(7)=K*U(6)*T_actual+U(4)*K*(U(1)+2*U(2)); 
 end

[P K]

Thank you @All . I tried with G=rand(1,10) and H=rand(1,10). It worked. I would find out why it is not working with MY G AND H.

[Torsten]

As a quick and dirty solution, add the line

global G H

in "eqn" as well as in the function of your program where you define G and H.