Change Algorithms 12.2 and 12.3 to accommodate the partial differential equation u / t 2 2u

Change Algorithms 12.2 and 12.3 to accommodate the partial differential equation
∂u / ∂t − α2 ∂2u / ∂x2 = 0, 0 < x < l, 0 < t;
u(0, t) = φ(t), u(l, t) = (t), 0< t;
u(x, 0) = f (x), 0≤ x ≤ l,
where f (0) = φ(0) and f (l) = Ψ(0).