We are interested in solving the advection equation where ,
with periodic boundary conditions and In the grid , .
using the forward euler method, or where is the approximation of at the grid points.
What I don't understand:
We are essentially using to calculate . Initially this is fine because is known for all , but how would we calculate ? we can't, since that would require us to know which doesn't exist. And this issue propagates, each new we can calculate one less point than .
What am I missing?