Practice 4-Step Adams–Bashforth Method - 15.3.4 | 15. Adams–Moulton Method | Mathematics - iii (Differential Calculus) - Vol 4
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4-Step Adams–Bashforth Method

15.3.4 - 4-Step Adams–Bashforth Method

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Practice Questions

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Question 1 Easy

What is the purpose of the Adams–Bashforth method?

💡 Hint: Think of what we aim for in numerical methods.

Question 2 Easy

What does 'step size' refer to in numerical methods?

💡 Hint: Consider how we define intervals between values.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the primary goal of the Adams-Bashforth method?

Calculate integrals
Solve ordinary differential equations
Optimize computational speed

💡 Hint: Focus on the specific application of this method.

Question 2

True or False: The local truncation error for the 4-step Adams-Bashforth method is \( O(h^4) \).

True
False

💡 Hint: Remember, local truncation error and global error are not always the same.

2 more questions available

Challenge Problems

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Challenge 1 Hard

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.

💡 Hint: Make sure to determine initial function evaluations needed for the formula before applying the 4-step method.

Challenge 2 Hard

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.

💡 Hint: Consider real-life scenarios where accuracy over time is crucial, such as weather predictions.

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