I've made a program that solves non-linear systems (2x2 and 3x3) of equations by newton method: r[i+1]=r[i]-J(r[i])^-1*F(r[i]).
The user is able to insert the functions (that I've set the program to store in FMEM - fn1, fn2...). During the iteration the values of each function will be in the vector F.
The big deal is defining the Jacobian Matrix. I wasn't able to find any way to make it unless the user insert by itself all the derivatives (4 or 9 functions) and the program allocate them, after calculating its values, in the matrix J.
Any suggestions or tips?