The data in the table below represents the altitude $H$ (in feet) of a small rocket that is launched vertically upward as a function of time $t$ (in seconds): $$\begin{array}{c|cccccccc} t\text{ (s)}&0&2&4&6&8&10&12&14\\ H\text{ (ft)}&0&80&350&800&1400&2100&3100&4100\\ \hline t\text{ (s)}&16&18&20&22&24&26&28&30\\ H\text{ (ft)}&5300&6500&7900&9300&10700&12200&13800&15300 \end{array}$$
- Develop a computer program to obtain the rocket's velocity $v$ and acceleration $a$ at each point using the finite-difference formulae with a truncation error of $O(h^2)$.
- Then, display the results in three plots (altitude vs. time, velocity vs. time and acceleration vs. time).
- Comment on the results you show in the plots!
I have to develop a program to obtain the rocket's velocity and acceleration at the same time instant, using finite difference formula of $O(h^2)$ truncation error.
Which type of finite difference method do I use (forward / backward / central) and (two / three / four point)? Moreover, what is the significance of truncation error in this context?