Practice Finite Difference Methods (fdm) (5.2) - Numerical Solutions of Partial Differential Equations

Practice: Finite Difference Methods (FDM)

Lesson 5.2Numerical Solutions of Partial Differential Equations

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9 questions

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Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What does discretization in FDM involve?
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Think about how you might measure a continuous quantity.
Question 2.
What is the forward difference approximation formula?
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Remember that it uses values at x and a small step h away.
3Question 3.
What is the primary function of Finite Difference Methods?
- To solve algebraic equations
- To approximate solutions of PDEs
- To perform integral calculus
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Remember what we discussed regarding the functions of FDM.
4Question 4.
True or False: Finite Difference Methods are limited to complex geometries only.
- True
- False
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Think about when we first introduced the methods.
Question 5.
Derive the FDM formula for the time-stepping in the heat equation starting from the original PDE.
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Carefully apply Taylor series expansions.
Question 6.
Discuss how the stability of the FDM solution can be affected by the choice of Δx and Δt.
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Review stability criteria linked with numerical methods.

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