Question

Consider the one dimensional heat equation with homogeneous Dirichlet conditions and initial condition:

PDE : ut = k uxx, BC : u(0, t) = u(L, t) = 0, IC : u(x, 0) = f(x)

a) Suppose k = 0.2, L = 1, and f(x) = 180x(1−x) 2 . Using the first 10 terms in the series, plot the solution surface and enough time snapshots to display the dynamics of the solution.

b) What happens to the solution as t → ∞? Explain your answer in light of (a) and the physical interpretation of the problem. Does (b) reflect this?

c) Redo parts (a) and (b) for k = 0.1, L = π, and f(x) = 2 cos

Answer 1