Practice Approximate Values Calculation (3.2) - Computational fluid dynamics (Contd.)

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9 questions

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

Question 1.
Define what a partial differential equation (PDE) is.
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Focus on what 'partial' means in the context of derivatives.
Question 2.
What does the parameter M indicate in PDE classifications?
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Recall the thresholds for M.
3Question 3.
What classification of PDE results from M < 1?
- Elliptical
- Parabolic
- Hyperbolic
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Recall the definitions for each classification.
4Question 4.
True or False: When M = 1, the PDE is hyperbolic.
- True
- False
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Think of how the discriminant behaves at M = 1.
Question 5.
Given a function phi(x, y) = x² + y², classify the PDE based on values of M = 0.5, M = 1, and M = 1.5.
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Calculate the discriminant for confirmation.
Question 6.
Using finite difference, find the approximate value of f(x) = sin(x) at x = π/4 using a delta of 0.1 and compare it to the actual value.
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Remember to calculate sin(π/4) exactly.

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