15.3.4 - 4-Step Adams–Bashforth Method
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Practice Questions
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What is the purpose of the Adams–Bashforth method?
💡 Hint: Think of what we aim for in numerical methods.
What does 'step size' refer to in numerical methods?
💡 Hint: Consider how we define intervals between values.
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Interactive Quizzes
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What is the primary goal of the Adams-Bashforth method?
💡 Hint: Focus on the specific application of this method.
True or False: The local truncation error for the 4-step Adams-Bashforth method is \( O(h^4) \).
💡 Hint: Remember, local truncation error and global error are not always the same.
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Challenge Problems
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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.
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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