Practice Summary Of Key Concepts (5.6) - Numerical Solutions of Partial Differential Equations

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10 questions

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Exercise
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6 sample questions

Question 1.
What does FDM stand for?
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Think about the method that uses differences.
Question 2.
Is FEM suitable for complex geometries?
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Remember, FEM = Flexible.
3Question 3.
What is the main advantage of FDM?
- Flexibility
- Simplicity
- Computational expense
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Consider ease of use.
4Question 4.
True or False: FEM is suitable for simple geometry problems.
- True
- False
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Think about what FEM is designed for.
Question 5.
Given a 1D heat equation, develop a finite difference scheme for a grid size of N=5 and a time increment Δt. Analyze stability conditions.
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Think about the relationships in the heat equation.
Question 6.
Apply FEM to a nonlinear dynamics problem in a 2D domain. Describe stepwise how you will approach the solution, including meshing.
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Focus on breaking down complex behaviors into manageable systems.

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