4.4.2 - Adams-Moulton Methods (Implicit Multistep)
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Practice Questions
Test your understanding with targeted questions
Define the term 'Adams-Moulton Methods'.
💡 Hint: Think about their main focus in solving equations.
What is the significance of using an implicit method?
💡 Hint: Consider how they utilize previous values.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the primary advantage of using Adams-Moulton methods?
💡 Hint: Recall how they use values from current and past steps.
The step size 'h' in the methods represents:
💡 Hint: Think about the interval in calculations.
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Challenge Problems
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Solve the ODE dy/dt = 3y with initial conditions y(0) = 1 using the Adams-Moulton method over the interval [0, 1] with step size h = 0.1. Show all steps.
💡 Hint: Remember to setup each calculation carefully and compute f values correctly.
Consider a stiff system modeled by the equation dy/dt = -5y, y(0) = 2. Use the Adams-Moulton method to find the solution at t = 1 using a step size of h = 0.2. Discuss how the method handles the stiffness.
💡 Hint: Identify how each step maintains boundedness despite the rapid changes.
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