Solve the following PDE:

∂²u/∂x² + b∂u/∂x = ∂u/∂t

Boundary conditions              u(0, l) = 0        u(1, l) = 0

Initial conditions                     u(x, 0) = 0        0 ≤ x ≤ 1

Use second-order accurate finite-difference analogues for the derivatives with a Crank-Nicolson formulation to integrate in time. Write a computer program for the solution. Increase the value of Δt by 10% for each time step to more quickly obtain the steady-state solution, and select values of Δx and Δt for good accuracy. Plot u versus x for various values of t. Solve for values of b = 4, 2, 0, - 2, - 4.