20.6. Summary

Try these first

1. 1.

   What is a Partial Differential Equation?

   Hint

   Think about how it differs from an ordinary differential equation.

2. 2.

   Name a type of PDE and give an example.

   Hint

   Recall the types we discussed: Elliptic, Parabolic, Hyperbolic.

3. 3.

   What does the acronym EPH stand for regarding types of PDEs?

   • Energy
   • Pressure
   • Heat
   • Elliptic
   • Parabolic
   • Hyperbolic
   • Equilibrium
   • Phase
   • Homogeneity

   Hint

   Recall the order in which we discussed the types.

4. 4.

   True or False: The Finite Volume Method ensures conservation laws.

   • True
   • False

   Hint

   Think about fluid dynamics where mass must be conserved.

5. 5.

   Derive the explicit finite difference scheme for the heat equation and analyze its stability.

   Hint

   Focus on the discretization of the heat equation and ensure you verify the conditions.

6. 6.

   Consider a PDE representing fluid flow in a channel. Discuss how the Finite Volume Method might apply to ensure mass conservation.

   Hint

   Envision how mass flows in and out of each controlled volume in your explanation.