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format long;

syms i imin n error y x h emin;

n = 30;

x = 0.5;

h = 1;

emin = 1;

for i =1:n

h = h*0.25;

y = [sin(x+h)-sin(x)]/h;

error(i) = abs(cos(x)-y);

i;

h;

y;

error;

TruncationError(i) = ((-1/6)*h^2*cos(x));

TotalError = ((-1/6)*h^2*cos(x)+error);

if error < emin

emin = error;

imin = i;

end

end

imin;

emin;

%hold on

%a = -log10(abs(error));

%b = log10(h);

%plot (a,b)

%plot (error);

%plot (TruncationError);

%plot (TotalError);

I'm new to matlab and am not sure how all the commands work. I am trying to plot error, truncation error, and total error all on the same graph. The x and y axis need to be what a and b are both log. It should look similar to the picture below numbers are different. Any guidance in the correct direction will be extremely helpful. Thanks.

dpb
on 12 Feb 2021

You've not saved the values of h in the loop to use to plot against -- but also note that at the end of your loop that h will be (1/4)^n --> (1/4)^30

>> (1/4^30)

ans =

8.6736e-19

>> log10(ans)

ans =

-18.0618

>>

so your log10(h) axis would go from 0 --> -19 instead of 0 --> 6

So unless the plot is mislabeled, it shows h went from ~10 to 10^6 instead.

There is also no need for symbolic variables here...

Rafael Hernandez-Walls
on 12 Feb 2021

Why don't you treat like this:

n = 30;

x = 0.5;

h(1) = 1;

emin = 1;

for i =1:n

if i==1

h(1)=0.5;

else

h(i) = h(i-1)*0.25;

end

y = [sin(x+h(i))-sin(x)]/h(i);

error(i) = abs(cos(x)-y);

TruncationError(i) = ((-1/6)*h(i)^2*cos(x));

TotalError(i) = ((-1/6)*h(i)^2*cos(x)+error(i));

if error(i) < emin

emin = error;

imin = i;

end

end

loglog(h,TotalError,'r')

figure

loglog(h,TruncationError,'k')

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