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

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 :-)

Answer 1

[Sriram Tadavarty]

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

[Savannah Phillips]

Hi Sriram,

do you mean like this?

for i = 1:10

h(i) = 10.^(-i);

end

When I change it to the above it doesn't work, though. What do you think?

[Sriram Tadavarty]

Hi Savannah, I made modification to the answer. Please look at it and let me know, if the same is expected.

[Savannah Phillips]

Ah, ok thank you. that works now! Thank you again :-)

Answer 2

[Pankaj Narayan Sawant]

Consider the function u(x) = e3x. Write Matlab/Python/Julia code to compute the