- Derive the equation for a parabolic fit to three grid points located at $x=0$, $x=\Delta x$ and $x=2\Delta x$.
- Why should you be careful using polynomial fits outside the fitted range of the data?
- For a uniform grid, write down or derive the simplified equation for the Trapezoid method.
- Does the Trapezoid method work for nonuniform grids?
- What is the convergence order of the Trapezoid method?
- What is the global convergence order of the Simpson’s method? (This is not in the notes. Do your own search.)
- The standard Simpson’s method requires an odd number of points. What is the preferred method if your interval has an even number of points?