Practice Adams-bashforth Methods (explicit Multistep) (4.4.1) - Numerical Solutions of Ordinary Differential Equations

Practice: Adams-Bashforth Methods (Explicit Multistep)

Lesson 4.4.1Numerical Solutions of Ordinary Differential Equations

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9 questions

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6 sample questions

Question 1.
What is the Adams-Bashforth method?
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Think about how it utilizes earlier function evaluations.
Question 2.
Define polynomial interpolation.
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What do we use to form polynomials?
3Question 3.
What type of method is Adams-Bashforth?
- Explicit Multistep
- Implicit Single Step
- None of the above
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Recall the acronym 'AB' and what it signifies.
4Question 4.
True or False: The Adams-Bashforth method only uses the most recent function evaluation.
- True
- False
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Think about how the method utilizes past data for predictions.
Question 5.
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).
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Start by finding the first evaluation using the derivative function provided.
Question 6.
In what scenarios might the Adams-Bashforth methods fail in terms of accuracy and stability? Provide specific examples.
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Think about the nature of stiff equations and how they interact with numerical methods.

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