Both 1 and 2

1 One-dimensional convection equation: analytical solution Find the solution at t = 1.5 of the one-dimensional convection equation. in r 2 0, with initial condition otherwise and boundary condition u(L| = 0) = 0, Plot the initial and u(t = 15,r) solutions. 2 One-dimensional convection equation: numerical solution Numerically integrate the one-dimensional convection equation, t0 in r E [0,1, with initial condition (t 0, 0 and boundary condition u(t,0 Discretize the spatial derivative using the three-point-stencil centered differences sin(4t) and choose an appropriate or Homework #2 to perform the time integration: e-sided finite difference at -1. Use the Runge Kutta method of - tu n+ 1 2 Set r 0.01 and t