Practice Multistep Methods - 4.4 | 4. Numerical Solutions of Ordinary Differential Equations | Numerical Techniques
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Multistep Methods

4.4 - Multistep Methods

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Practice Questions

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Question 1 Easy

What are multistep methods?

💡 Hint: Think about how many points are involved in making these calculations.

Question 2 Easy

Name a type of multistep method.

💡 Hint: Recall the names mentioned in class.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the main characteristic of multistep methods?

They use only the current point
They use multiple previous points
They are only for stiff equations

💡 Hint: Think about how they differ from single-step methods like Euler's.

Question 2

True or False: Adams-Moulton methods are usually more stable than Adams-Bashforth methods.

True
False

💡 Hint: Consider the impact of implicitness on stability.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given the differential equation dy/dt = -2y with an initial condition y(0) = 1, use the two-step Adams-Bashforth method with a step size of 0.1 to estimate y(0.2).

💡 Hint: Start with the simplest method to get the intermediate result before applying the multistep technique.

Challenge 2 Hard

Consider the stiff ordinary differential equation dy/dt = -y^2 + 3y. Solve it using the Adams-Moulton method with initial values and a given step size.

💡 Hint: Focus on constructing the system of equations for the implicit steps and remember to consider the previous values.

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