Matlab code help!

Use fourth order accurate centered finite difference formulas for the second derivative to compute the derivative directly from the data. Use second order forward difference formulas for the first two points and second order backward difference formulas for the last two points.

Use MATLAB's gradient function twice on the data.

Use MATLAB's gradient function twice on interpolated data generated with a clamped spline with a derivative set to 0 at both ends and 0.5 inch increments in x.

The function should have three column vector outputs:

1. The bending moment values M(x) calculated using 4th order centered finite difference formulas.

2. The bending moment values M(x) calculated using the gradient function on the data.

3. The bending moment values M(x) calculated using the gradient function on the clamped spline interpolation of the data.

Only output 2 is correct.

Here is my code:

function [M_Oh4_FD, M_gradient, M_grad_spline] = student_solution(beam_deflection_data)

% Constants

E = 29.0E6; % psi

I = 156; % in^4

% Extract data

x = beam_deflection_data(:, 1);

v = beam_deflection_data(:, 2);

% Calculate h

h = x(2) - x(1);

n = length(v);

v_diff2 = zeros(n, 1);

% 2nd order forward difference for first two values

v_diff2(1) = (-v(4) + 4*v(2) - 5*v(2) + 2*v(1))/(h^2);

v_diff2(2) = (-v(5) + 4*v(4) - 5*v(3) + 2*v(2))/(h^2);

% 2nd order backward difference for last two values

v_diff2(n-1) = (2*v(n-1) - 5*v(n-2) + 4*v(n-3) - v(n-4))/(h^2);

v_diff2(n) = (2*v(n) - 5*v(n-1) + 4*v(n-2) - v(n-3))/(h^2);

% Calculate second derivative using 4th order centered finite difference scheme

for i = 3:n-2

v_diff2(i) = (-v(i+2) + 16*v(i+1) - 30*v(i) + 16*v(i-1) - v(i-2)) / (12*h^2);

end

M_Oh4_FD = (E*I)*v_diff2;

% Compute second derivative using gradient function on the data

dvdx = gradient(v, h);

d2vdx2 = gradient(dvdx, h);

M_gradient = (E*I)*d2vdx2;

% Compute M_grad_spline using clamped spline interpolation

x_interp = x(1):0.5:x(end);

v_clamp = zeros(n+2, 1);

v_clamp(2:end-1) = v;

cs = spline(x, v_clamp, x_interp);

dvidx = gradient(cs, h);

d2vidx2 = gradient(dvidx, h);

M_grad_spline = (E*I)*d2vidx2;

end