Practice 3-step Adams–bashforth Method (153.3) - Adams–Moulton Method - Mathematics - iii (Differential Calculus) - Vol 4

Practice: 3-Step Adams–Bashforth Method

Lesson 153.3Adams–Moulton Method

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9 questions

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6 sample questions

Question 1.
Define the 3-step Adams-Bashforth method in your own words.
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Think about how it employs past values.
Question 2.
What is the formula for the 3-step Adams-Bashforth method?
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Recall how the coefficients come from interpolation.
3Question 3.
What does the 3-step Adams-Bashforth method rely on?
- Past two function values
- Three past function values
- All past function values
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Refer back to the definition of this multistep method.
4Question 4.
The global error of the 3-step Adams-Bashforth method is:
- True
- False
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Think about the relationship between local and global errors.
Question 5.
Given the equation dy/dx = sin(x) + cos(y), y(0)=0, compute y(0.5) using the Adams-Bashforth method with h = 0.1. Include all intermediate calculations.
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Ensure you derive the initial values correctly before applying the multistep method.
Question 6.
Analyze how changing the step size h affects the accuracy and stability of the 3-step Adams-Bashforth method when solving dy/dx = e^{-x} - y.
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Consider how lower step sizes generally improve accuracy but at the cost of computational load.

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