Practice How Euler’s Method Works (4.2.2) - Numerical Solutions of Ordinary Differential Equations

Practice: How Euler’s Method Works

Lesson 4.2.2Numerical Solutions of Ordinary Differential Equations

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8 questions

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6 sample questions

Question 1.
What does Euler's method approximate?
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Think about the type of equations we are solving.
Question 2.
What is the initial condition?
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Where do we start in our calculations?
3Question 3.
What is the formula for Euler's method?
- y(n+1) = y(n) + h * f(t(n)
- y(n))
- y(n+1) = y(n) - h * f(t(n)
- y(n))
- y(n+1) = y(n) + f(t(n)
- h)
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Remember the structure of the formula.
4Question 4.
True or False: Euler's method is a higher-order numerical method.
- True
- False
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Consider what 'first-order' means in terms of numerical methods.
Question 5.
Using Euler's method with step size h = 0.2, approximate the value of y(1.0) for y' = 3y with the initial condition y(0) = 1. Run calculations for five steps.
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Keep tracking your values using the Euler update formula.
Question 6.
If we change the step size to h = 0.5 in the previous problem, how does it affect the accuracy of y(1.0)? Discuss.
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Reflect on how step sizes influence results in numerical methods.

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