Practice Numerical Solutions Of Odes (15) - Adams–Moulton Method - Mathematics - iii (Differential Calculus) - Vol 4

Practice: Numerical Solutions of ODEs

Lesson 15Adams–Moulton Method

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10 questions

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6 sample questions

Question 1.
What does the acronym IVP stand for?
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Think about how we begin solving differential equations.
Question 2.
What is meant by step size in numerical methods?
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It's related to how quickly we move along the x-axis.
3Question 3.
What type of method is the Adams-Bashforth method?
- Implicit
- Explicit
- Neither
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Recall the key features of Adams-Bashforth.
4Question 4.
True or False: The Local Truncation Error for a 2-step Adams-Bashforth method is O(h^2).
- True
- False
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Consider the definition of Local Truncation Error.
Question 5.
Given the ODE $\frac{dy}{dx} = y + 3x^2$ with initial condition $y(0)=1$ , apply the 4-step Adams-Bashforth method to compute an approximation to $y(0.6)$ using a step size of $h=0.2$ . Start with values obtained from a single-step method.
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Don’t forget to derive initial values before applying the 4-step method.
Question 6.
Critically analyze how increasing the number of steps in the Adams-Bashforth method affects accuracy and computational load. Provide a practical scenario where one might choose a higher or lower step count.
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Reflect on typical use-cases for rapid versus precise results.

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