1) Given the following partial differential equation, along with initial conditions and boundary conditions, solve the first two time steps using the Explicit Method. Sketch the solution (plot T(x,t) vs. x) at initial conditions, after each time step, and at the expected steady state. Note that the Central Difference approximation (2nd Order) for ∂T/∂x is to be used to represent derivative boundary conditions.
k ∂²T/∂x² = ∂T/∂t ; k = 3; 0 ≤ x ≤ 1; Δx = 1/3; Δt = 1/100
I.C.: T(x,0) = 0
B.C.: ∂T/∂x(0,t) = -0.5, T(1,t) = 0.8
