Practice Algorithm: Adams–Moulton Method (Predictor–Corrector) - 16.5 | 16. Error Analysis in Numerical ODE Solutions | Mathematics - iii (Differential Calculus) - Vol 4
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16.5 - Algorithm: Adams–Moulton Method (Predictor–Corrector)

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the main benefit of using the Adams-Moulton method over explicit methods?

💡 Hint: Think about how implicit methods generally perform.

Question 2

Easy

What does a predictor do in a predictor-corrector scheme?

💡 Hint: Consider the flow of how solutions are derived.

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 is an advantage of the Adams-Moulton method?

  • A. It is faster than explicit methods
  • B. It has higher accuracy
  • C. It requires fewer computational steps
  • D. It cannot solve stiff ODEs

💡 Hint: Think about the benefits of implicit methods.

Question 2

True or False: The Adams-Moulton method requires initial values from a one-step method.

  • True
  • False

💡 Hint: Consider how starting points are critical for multistep methods.

Solve and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Given the ODE dy/dx = y - x^2 + 1, with y(0)=0.5, use the 1-Step Adams-Moulton method to find y at x=0.2 with a step size h=0.1. Show all steps and iterations.

💡 Hint: Pay attention to the function's evaluation at each required point.

Question 2

In solving a stiff ODE using both Euler and Adams-Moulton methods, describe the performance difference in terms of accuracy and stability based on your findings.

💡 Hint: Consider how stiffness influences behavior in numerical schemes.

Challenge and get performance evaluation