Hi Abhi,
I understand that you are trying to use the finite difference method to calculate the derivative of v_phi w.r.t r. A few salient points I noticed about your code:
1) Your representation of the partial derivative of v_phi w.r.t r is only valid if r is the only independent variable of which v_phi is defined. If there are other variables involved, then d(v_phi) is not the same as partial derivative of v_phi.
2) Assuming that your representation is valid, I understand that y is the RHS of the equation and y1 is the LHS of the equation. If so, the representation of y1 is incorrect. The correct formula should be:
y1(i)= ( ( v_phi(i+1)-v_phi(i) / r(i+1)-r(i) ) - ( v_phi(i) / r(i) ) );
3) Ensure that the limits of the for loop are defined correctly between 1 and n-1, where n is the size of the array v_phi. Something like this:
v_phi = [36.99 37.00 35.78 31.43 26.91 23.32 19.46 16.97 14.49 12.12 10.42 8.52 7.25 6.06 5.11 3.92 3.30 2.54 2.11 1.42 1.46 1.46 0.97 0.63 0.63 0.51 0.40 0.91 0.24 0.36 0.63 0.71 0.45 0.26 0.74 ];
r = [3.59 3.76 3.94 4.12 4.29 4.47 4.65 4.82 5.00 5.18 5.35 5.53 5.71 5.88 6.06 6.24 6.41 6.59 6.76 6.94 7.12 7.29 7.47 7.65 7.82 8.00 8.18 8.35 8.53 8.71 8.88 9.06 9.24 9.41 9.50 ];
y=[];
y1=[];
for i = 1:1:size(v_phi,2)-1
y(i) = (r(i))*((( v_phi(i)/ r(i)) -( v_phi(i+1)/r(i+1)) )/(r(i+1)-r(i)) );
y1(i)= ( ( v_phi(i+1)-v_phi(i) / r(i+1)-r(i) ) - ( v_phi(i) / r(i) ) );
end
Ensure to define y and y1 as empty arrays before the for loop.
Regards,
Arvind
