Plotting log x and y

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]

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...

Answer 1

[Rafael Hernandez-Walls]

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')