20.2.1. Finite Difference Method (FDM)

Try these first

1. 1.

   What does FDM stand for?

   Hint

   Think about how we approximate derivatives.

2. 2.

   Name a common application of FDM.

   Hint

   Consider phenomena modeled by PDEs.

3. 3.

   What does the acronym FDM stand for?

   • Finite Difference Method
   • Finite Derivative Method
   • Functional Difference Method

   Hint

   Think of how we approximate derivatives.

4. 4.

   True or False: The explicit method in FDM is unconditionally stable.

   • True
   • False

   Hint

   Recall the conditions for stability in explicit methods.

5. 5.

   Using FDM, solve the 1D heat equation with boundary conditions u(0,t)=0 and u(L,t)=100 over a domain of length L=10 with appropriate discretization.

   Hint

   Draw out the grid and apply the finite difference formulas.

6. 6.

   Propose a method to overcome the stability issues of explicit methods when implementing FDM. Discuss the advantages and potential limitations.

   Hint

   Consider stability versus computational cost when discussing methods.