differential Equations with ode45

Hi! Please help solve the differential equation with ode45. The problem is: I can't find Uk (it's value Vy in the previous step).

    function odefun100
    t0=0;
    tk=0.05;
    [T,Y]=ode45(@odefun12, [t0 tk],0);
    nT=numel(T);
     Vy=zeros(nT,1);
    L1=zeros(nT,1);
    L=zeros(nT,1);
    Uk=zeros(nT,1);   
    for ik=1:nT
    [~,Vy(ik,1),L1(ik,1),L(ik,1),Uk(ik,1)]=odefun12(T(ik),Y(ik,:));
    end

    plot(T,Vy,T,Uk)

    function [dy, Vy, L1 L Uk]=odefun12(t,y)
    N=0;
    Uk=0;

    Uk=N;
    L2=y(1);

    E=randn;

    b=exp(-0.1*0.1);
    Vy=b*Uk + 2*sqrt(1-b^2)*E;

    L1=0.006*Vy;

    dy=zeros(1,1);
    dy(1)=0.01*Vy-5*L2;

    L=L1+L2;

    N=Vy;
    end
    end

Why Uk=0?

Answer 1

[Orion]

Hi,

you wrote :

      function [dy, Vy, L1 L Uk]=odefun12(t,y)
      N=0;
      Uk=0;

      Uk=N;

=> Uk = N = 0 whatever the inputs are.

you forget to code something

[Alex Pak]

thank you, you are right, but I need Uk, Uk is Vy, but on the previous step of calculating.

I know how to solve this problem in the simple case. For example:

    N=0;
    Uk=0;
    x=0:9;
    for i=1:10;   
    Uk(i)=N;
    E(i)=randn;
    b=exp(-0.1*0.1);
    Vy(i)=b*Uk(i) + 2*sqrt(1-b^2)*E(i);
    N=Vy(i);
    end
    plot(x,Vy,x,Uk)

Please tell me, how can I solve this problem with ode45?