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Forward and central difference help - loglog plot of errors vs h

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Hi! If anyone is able, I'd really appreciate help on this coursework I'm stuck on. The question is
Within your file, test your difference quotient formulas with h = 10^(−i) for i = 1, 2, . . . , 10. Plot the errors versus h in a figure with double-log axes. Can you observe the expected rate of convergence (asymptotic behaviour as h → 0)? What happens for very small h?
My code is this
f = @(x) sin(x); %function handle
for i = 1:10
h = 10.^(-i);
end
[fd,cd] = FDCD(f, 0.9, 10.^(-i));
% f'(0) = 1 for this question
errors = 1 - fd; % Approximation error for forward difference quotient
% Setting the figure
figure
loglog(errors, h);
% Formatting the plot
(just title, axes labels, etc)
When I run the code, the graph appears, formatted etc, but there's no points/lines. I'm not sure what I need to do. I'm fairly certain my function [fd,cd] (a function for forward and central difference quotient) is correct. I've got it on another tab and it's just
function [fd,cd] = FDCD(f,x,h)
% forward-difference quotient
fd = (f(x + h) - f(x))/h;
% central-difference quotient
cd = (f(x + h) - f(x - h))/2.*h;
If anyone can spot what I'm doing wrong, I'd really appreciate it. Thank you :-)

Accepted Answer

Sriram Tadavarty
Sriram Tadavarty on 17 Mar 2020
Edited: Sriram Tadavarty on 17 Mar 2020
Hi Savvanah,
In the for loop, h is over written with the last value. I feel that is the issue in the code. Update with h(i) instead of h in the for loop. And then call the FDCD function in the for loop. Here is the code that does the modifications mentioned
for i = 1:10
h(i) = 10.^(-i);
[fd(i),cd] = FDCD(f,0.9,h(i));
end
Hope this helps.
Regards,
Sriram
  3 Comments
Sriram Tadavarty
Sriram Tadavarty on 17 Mar 2020
Hi Savannah, I made modification to the answer. Please look at it and let me know, if the same is expected.

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More Answers (1)

Pankaj Narayan Sawant
Pankaj Narayan Sawant on 9 Sep 2021
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