Richardson extrapolation matlab error

[Adrian Soo]

Hi everyone, I am trying to differentiate a function by means of Richardson Extrapolation in MATLAB. However, I could not run the program. Here are the outputs and its codes. Could anyone explain to me
what is my mistake? The codes are based on "Numerical Methods Using MATLAB by John H. Matthews and
Kurtis D. Fink (International Edition)".

>> f = @(x) x^2;
>> toler = 0.005;
>> function [L,n] = difflim(f,x,toler)
function [L,n] = difflim(f,x,toler)
|
Error: Function definitions are not permitted in this context.

=========================================
M-file:

function [L,n] = difflim(f,x,toler)
%Input - f is the function input as a string 'f'
% - x is the differentiation point
% - toler is the tolerance for the error
%Output - L=[H' D' E']
% H is the vector of step sizes
% D is the vector of approximate derivatives
% E is the vector of error bounds
% n is the coordinate of the "best approximation"
max1 = 15;
h = 1;
H(1) = h;
D(1) = (feval(f,x+h)-feval(f,x-h))/(2*h);
E(1) = 0;
R(1) = 0;

for n = 1:2
h = h/10;
H(n+1) = h;
D(n+1) = (feval(f,x+h)-feval(f,x-h))/(2*h);
E(n+1) = abs(D(n+1)+abs(D(n))+eps);
end

n = 2;

while((E(n)>E(n+1))&(R(n)>toler))&n<max1
h=h/10;
H(n+2)=h;
D(n+2)=(feval(f,x+h)-feval(f,x-h))/(2*h);
E(n+2)=abs(D(n+2)-D(n+1));
R(n+2)=2*E(n+2)/(abs(D(n+2))+abs(D(n+1))+eps);
n=n+1;
end

n=length(D)-1;
L=[H' D' E'];

 

[mighty2000]

Hi there,

I see that you are trying to use Richardson Extrapolation in MATLAB to differentiate a function. However, it seems like you are getting an error when trying to run the program. Looking at the codes, I can see that the error is occurring because you are trying to define a function within another function. This is not allowed in MATLAB.

To fix this issue, you can either move the function definition outside of the difflim function or create a separate .m file for the function and call it within the difflim function.

Additionally, I noticed that you are using the eps function to calculate the error bound. This function returns the machine epsilon, which may not be accurate enough for your desired tolerance. I would suggest using a more precise value for the error bound, such as 10^-15.

I hope this helps and good luck with your project!