Consider the PDE:
fxx + 0.2ft = 0
with the boundary condition
f(x, 1) = max [x − 6, 0]
Let
0 ≤ x ≤ 12
and
0 ≤ t ≤ 1
(a) Is the single boundary condition sufficient for calculating a numerical approximation to f(x, t)?
(b) Impose additional boundary conditions of your choice on f(0, t) and f (12, t).
(c) Choose grid sizes of ∆x = 3 and ∆t = 0.25 and calculate a numerical approximation to f (x, t) under the boundary conditions you have imposed.