Parabolic Partial Differential Equations

• Write the canonical parabolic PDE, the unsteady 1D diffusion equation
• What ODE method is FTCS similar to?
• What ODE method is BTCS similar to?
• What ODE method is Crank Nicholson (CN) similar to?
• What are the time and space discretization orders of FTCS, BTCS, and CN?
• Consider the stencils for the methods discussed.
  • What do these imply about the domain coupling and rate of propagation of information?
  • How would this change if you used a higher order stencil?
• Why is the method of lines called that?
• True or False: the treatment of boundary conditions for simple PDEs is basically the same as for ODE BVPs.
• Consider how index arrays can be used to good effect in Python (or Julia) to simplify the implementation and avoid loops (which are costly in Python).