Homework #6

1.

(a) Is it possible to obtain an approximation to $y^{\prime\prime}(0)$ with error = $O(h^2)$ using $y(0)$, $y(h)$, $y(2h)$? Either way, support your result with a calculation.

(b) How about with the values $y(0)$, $y(h)$, $y(2h)$ $y(3h)$? If so, find the formula.

2.

Ackleh et al. Exercise 10.3.6 (small Galerkin)

Extra credit: Extend the basis to $\{ \sin(\pi x),\ \sin(2\pi x), ... , \sin(N\pi x) \}$ and explore how the error depends on $N$.