PLEASE HELP with Forward, backward, and central difference approximations?

Question

equinox 2017-2-5

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https://ww2.mathworks.cn/matlabcentral/answers/323423-please-help-with-forward-backward-and-central-difference-approximations

回答： Image Analyst 2017-2-5

Hi I am really confused on how to approach this problem, I have started a little but am really not sure where to go from here so any help would be appreciated.

Consider the function f(x) =(1+ x^2 )^-1 defined on [-5, 5] . Choose equally-spaced grid points xi = -5+ih, where i=0,..,n and h=10/n with n= 11,21,51,101.

Approximate f'(xi) for i=1,..,n-1 using forward difference, backward difference, central difference approximations. Plot the results.

So far this is what i have:

 f = @(x) ((1+x.^2).^(-1)); 
 fprime = @(x) (-2*x)./((1+x.^2).^(2));
 n=11;21;51;101;
 h=10/n;
for i=1:n+1
  x(i)=-5+(i-1)*h
end
 x=linspace(-5,5,x(i));

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Answer 1

Image Analyst 2017-2-5

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https://ww2.mathworks.cn/matlabcentral/answers/323423-please-help-with-forward-backward-and-central-difference-approximations#answer_253425

在 MATLAB Online 中打开

You need brackets around the list of numbers where you define n. And you need to have the computation of h in a loop. See if this makes sense:

f = @(x) ((1+x.^2).^(-1));
fprime = @(x) (-2*x)./((1+x.^2).^(2));
n = [11;21;51;101]
h = 10 ./ n
for nIndex = 1 : length(n)
  this_n = n(nIndex)
  % for this value of n...
  % Compute this value of h...
  this_h = 10 / this_n
  % Now loop over i to compute x...
  for i = 1 : this_n
    x(i) = -5 + i * this_h
  end
end