Practice 4-step Adams–bashforth Method (15.3.4) - Adams–Moulton Method

Practice: 4-Step Adams–Bashforth Method

Lesson 15.3.4Adams–Moulton Method

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10 questions

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6 sample questions

Question 1.
What is the purpose of the Adams–Bashforth method?
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Think of what we aim for in numerical methods.
Question 2.
What does 'step size' refer to in numerical methods?
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Consider how we define intervals between values.
3Question 3.
What is the primary goal of the Adams-Bashforth method?
- Calculate integrals
- Solve ordinary differential equations
- Optimize computational speed
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Focus on the specific application of this method.
4Question 4.
True or False: The local truncation error for the 4-step Adams-Bashforth method is $O(h^4)$ .
- True
- False
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Remember, local truncation error and global error are not always the same.
Question 5.
Given the initial value problem $\frac{dy}{dx} = x + y$ with $y(0)=1$ , estimate $y(0.1)$ using the 4-Step Adams-Bashforth method. Calculate required initial values using a basic method first.
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Make sure to determine initial function evaluations needed for the formula before applying the 4-step method.
Question 6.
Evaluate how a larger step size would affect the accuracy of the Adams–Bashforth method in a long-term integration scenario. Provide examples to illustrate your response.
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Consider real-life scenarios where accuracy over time is crucial, such as weather predictions.

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