Initial Value of y(0)=0

How does one write a code for the IVP of y(0) = 0? The program won't accept the following. Also, can someone check my syntax for the equations I've entered? Thanks!

     function ystar = Eulermethod201(n)
    a=0;
    b=5;
    h=(b-a)/n;
    t=0:h:5;%Initialize time variable

    clear ystar;%wipe out old variable
    ystar(0)=0;%Initial condition (same for approximation)

    for i=0:length(t), %Set up "for" loop
        %Calculate the derivative
        k1=(-0.5*exp(t(i)/2)*sin(5*t(i))+5*exp(t(i)/2)*cos(5*t(i))-ystar(i));
        ystar(i+1)=ystar(i)+h*k1;%Estimate new value of y
    end
    %Exact solution
    y=(exp(t/2))*(sin(5*t));

    %Error calculation
    percent_error=100*abs(y-ystar)./y;
    disp(percent_error);
    %Plot approximate and exact solutions
    plot(t,ystar,'b--',t,y,'r-',t,percent_error,'g'); 
    legend('Approximate','Exact','Error');
    title('Euler Approximation n=50');
    xlabel('Time');
    ylabel('y*(t), y(t)');

Answer 1

[Fangjun Jiang]

Unlike C language, MATLAB uses 1-based index for vector and matrix. So if you define a 10x1 vector, a=rand(10,1), you refer it as a(1), a(2) till a(10).

If you have the need to indicate some value at time==0, you will need to use some kind of offset to deal with it.

[Karen]

If y(0)=0 is an initial value, then what type of offset would work in that situation? Does that mean that I can use y(1) = 0? Or subtract one as in i=1:length(t)-1; and also use y(1)=0? I've tried using y(.000001)=0, but I get the same error message as if I used y(0)=0.

[Fangjun Jiang]

Yes. You can't use y(0)=0 in MATLAB. You will need to do something like this for example

t=0:9;

y=10:10:100;

For any index number i, y(i) always corresponds to t(i), where i is a number from 1 to 10.