Consider the PDE:
fxx + .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 = .25 and calculate a numerical approximation to f(x, t) under the boundary conditions you have imposed.