3.1. Finite Difference Method

Try these first

1. 1.

   What are the three types of PDEs?

   Hint

   Think of the acronym EPH.

2. 2.

   Define boundary conditions.

   Hint

   Consider how they affect the solution.

3. 3.

   What is the domain of influence in a PDE?

   • A region dependent on point P
   • The entire solution domain
   • An irrelevant area

   Hint

   What impacts every point?

4. 4.

   True or False: The finite difference method is used exclusively for elliptic PDEs.

   • True
   • False

   Hint

   Think about the types of PDEs we discussed.

5. 5.

   Given a parabolic PDE, describe how you would set up the boundary and initial conditions for a simulation. What challenges might arise?

   Hint

   Consider how time evolves and how boundary constraints work.

6. 6.

   How might the behavior of a wave (hyperbolic PDE) differ from the steady-state of heat distribution (elliptic PDE) in terms of influence and dependence?

   Hint

   Think about how disturbances travel versus repeating states.