I have a data set whose second derivative I want to compute numerically, which can be obtained by $f''(x) \approx \displaystyle\frac{f(x+h) - 2f(x) + f(x-h)}{h^2}$.
My question is: given that I have values of the second derivative, can I solve for the original function and how many initial conditions do I need?
You solve a second order ODE with two initial conditions. I wonder how you would perform this operation numerically given $f''(x)$.
Your insights are appreciated.
You can take anti derivative of second order differentiation two times respectively with constants $C1 and c2$ to get original solution.