Euler Method Approximation Not Working

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Ali
Ali 2021-12-17
评论： Ali 2021-12-17
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

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回答（1 个）

Voss
Voss 2021-12-17
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.

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