4.4.1 - Adams-Bashforth Methods (Explicit Multistep)
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Practice Questions
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What is the Adams-Bashforth method?
💡 Hint: Think about how it utilizes earlier function evaluations.
Define polynomial interpolation.
💡 Hint: What do we use to form polynomials?
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Interactive Quizzes
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What type of method is Adams-Bashforth?
💡 Hint: Recall the acronym 'AB' and what it signifies.
True or False: The Adams-Bashforth method only uses the most recent function evaluation.
💡 Hint: Think about how the method utilizes past data for predictions.
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Challenge Problems
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Estimate the solution of the ODE dy/dt = 2y with an initial condition y(0) = 1 using the two-step Adams-Bashforth method, given a step size h = 0.1. Provide the calculations for y(0.1) and y(0.2).
💡 Hint: Start by finding the first evaluation using the derivative function provided.
In what scenarios might the Adams-Bashforth methods fail in terms of accuracy and stability? Provide specific examples.
💡 Hint: Think about the nature of stiff equations and how they interact with numerical methods.
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