Practice Finite Difference Method (fdm) (19.10.1) - Modelling – Membrane, Two-Dimensional Wave Equation

Practice: Finite Difference Method (FDM)

Lesson 19.10.1Modelling – Membrane, Two-Dimensional Wave Equation

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10 questions

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6 sample questions

Question 1.
What does the Finite Difference Method (FDM) help solve?
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Think about where analytical solutions might be challenging.
Question 2.
Define the CFL Condition in your own words.
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Consider what happens if that condition is violated.
3Question 3.
What is the primary purpose of the Finite Difference Method?
- To solve linear equations.
- To approximate solutions to differential equations.
- To create graphical representations of data.
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Think about what FDM is often applied to.
4Question 4.
True or False: The CFL condition is used to ensure the validity of numerical solutions.
- True
- False
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Consider stability aspects of numerical methods.
Question 5.
Given a grid where Δx = 0.05 m, Δy = 0.05 m, and Δt = 0.01 s, derive the CFL condition parameters for a wave speed of 300 m/s. Determine if the condition is satisfied.
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Focus on calculating each part, ensuring you respect the parameters set.
Question 6.
Apply the explicit finite difference method to find the displacement at the next time step for a given set of initial values un_i,j=2, un-1_i,j=1, un_i,j+1=3, and un_i,j-1=0. Define the neighboring contributions as well.
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Make sure to plug in all grid point values correctly and perform the appropriate calculations.

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