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

3 views (last 30 days)
Savannah Phillips on 17 Mar 2020
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 :-)

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 CommentsShow 1 older commentHide 1 older comment
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.
Savannah Phillips on 17 Mar 2020
Ah, ok thank you. that works now! Thank you again :-)

Pankaj Narayan Sawant on 9 Sep 2021
Consider the function u(x) = e3x. Write Matlab/Python/Julia code to compute the