Practice Numerical Solutions of ODEs - 15 | 15. Adams–Moulton Method | Mathematics - iii (Differential Calculus) - Vol 4
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Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What does the acronym IVP stand for?

💡 Hint: Think about how we begin solving differential equations.

Question 2

Easy

What is meant by step size in numerical methods?

💡 Hint: It's related to how quickly we move along the x-axis.

Practice 4 more questions and get performance evaluation

Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

What type of method is the Adams-Bashforth method?

  • Implicit
  • Explicit
  • Neither

💡 Hint: Recall the key features of Adams-Bashforth.

Question 2

True or False: The Local Truncation Error for a 2-step Adams-Bashforth method is O(h^2).

  • True
  • False

💡 Hint: Consider the definition of Local Truncation Error.

Solve 2 more questions and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

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.

💡 Hint: Don’t forget to derive initial values before applying the 4-step method.

Question 2

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.

💡 Hint: Reflect on typical use-cases for rapid versus precise results.

Challenge and get performance evaluation