Euler Method Approximation Not Working

Hello,

I am trying to plot a loglog error of the Euler IVP method. Everything works except for one issue. My approximation is always zero. I don't know why.

function error_euler

yfun = dsolve('Dy=t+y', 'y(0)=0', 't');
disp(['The IVP is Dy = t+y and the solution of IVP is ']);
disp(['y='])
disp(yfun);
f=@(t,y)t+y;
t0=0;
w0=0;
disp(['--------------------'])
disp(['       Step Size        Exact Solution          Approximation         Error'])
disp(['--------------------'])

for i=1:6
    a(i)=0;
    w1(i)=0;
    h(i)=0;
    t(i)=0;
end

for k=0:5
    h(k+1)=h(k+1)+0.1*2^-k;
    t=h(k+1);
    a(k+1)=a(k+1)+eval(yfun);
    w1(k+1)=w1(k+1)+h(k+1)*f(t0,w0);
end

for k=1:6
    disp([h(k)   a(k)   w1(k)   abs(a(k)-w1(k))])
end

loglog(h,abs(a-w1))
xlabel('h')
ylabel('Error')
grid on
title('Global Error Log-Log Plot')
end

You can see below that the approximation is zero. What am I doing wrong?

--------------------

Step Size Exact Solution Approximation Error

--------------------

0.100000000000000 0.005170918075648 0 0.005170918075648

0.050000000000000 0.001271096376024 0 0.001271096376024

0.025000000000000 0.000315120524429 0 0.000315120524429

0.012500000000000 0.000078451540634 0 0.000078451540634

0.006250000000000 0.000019572003762 0 0.000019572003762

0.003125000000000 0.000004887902739 0 0.000004887902739

Answer 1

[Voss]

Take a look at how the approximation is calculated:

w1(k+1)=w1(k+1)+h(k+1)*f(t0,w0);

You are always evaluating f at t0,w0.

[Ali]

Thank you! I didn't notice that.