Obtaining a fourth order of accuracy approximation formula for y''(0) and findind rhe unknown coefficients

I want to obtain a fourth order of accuracy approximation formula for y''(0). I want to create MATLAB application to find the unknown coefficients. I wrote a code but I could not declare function so I could not display function and find the unknown coefficiets. The code I wrote it as follows:

How can I declare and display the function ? Thanks for everything.

function accuracyapprox()
syms h;
A = [1 1 1 1 1 1; ...
    0 h 2*h 3*h 4*h 5*h; ...
    0 h^2/2 2*h^2 9*h^2/2 8*h^2 25*h^2/2; ...
    0 h^3/6 8*h^3/6 27*h^3/6 64*h^3/6 125*h^3/6; ...
    0 h^4/24 16*h^2/24 81*h^4/24 256*h^4/24 625*h^4/24; ...
    0 h^5/120 32*h^5/120 243*h^5/120 1024*h^5/120 3125*h^5/120];
B = [0 0 1; 0 0 0];

R = inv(A) * B;
end

[Jan]

You ask for an approximation of y''(0), but do not provide y, but R=inv(A)*B. What is unknown? What does "I could not declare function" mean? A function for what?

By the way, this is not twitter: No # before the tags, please.

[John D'Errico]

#removed, tags repaired.

[Kerem Candangil]

I understood. I wanted to ask how we can give matrix realization. Also I wanted to ask how we can construct second order of accuracy difference scheme for numerical solution.

Answer 1

[John D'Errico]

Save this function as an m-file, NOT in the MATLAB directories, but on your search path.

function ypp = accuracyapprox
  syms h
  A = ((0:5)*h).^((0:5).')./factorial(0:5).';
  ypp = pinv(A)*[0;0;1;0;0;0];

Now, use the function.

ypp = accuracyapprox
ypp =
  15/(4*h^2)
 -77/(6*h^2)
 107/(6*h^2)
     -13/h^2
 61/(12*h^2)
  -5/(6*h^2)