Consider a 3-point one dimensional stencil, consisting of the points
(i),
.
Construct the highest-order difference formula of the
second derivative at the point (i) which does not involve any other
second-order derivatives. You may include first-order derivatives,
however, as well as function values at the three points. Also, compute the
truncation error.
What is the computational work to compute such a derivative on an N-point
grid with periodic boundary conditions?