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3 cards from this section. Quick, good the night before a test.
Define what an implicit method is.
Think about what part of the equation depends on future information.
What is the main use of the Adams-Moulton method?
What type of equations do we often deal with in differential equations?
What type of method is the Adams-Moulton method?
Recall what makes a method implicit.
True or False: The Adams-Moulton method is only used for non-stiff ODEs.
Think about the applications of these methods.
If given the ODE dy/dx = y - x^2 + 1 and the initial condition y(0) = 0.5 with a step size of 0.1, apply the Adams-Moulton method to estimate y(0.1). Show all steps.
Make sure you derive initial values correctly and remember to apply the implicit nature during corrections.
For a stiff ODE, describe how you would adapt the Adams-Moulton method to ensure stability in your solution, particularly addressing step sizes.
What strategies can you use to control step sizes?
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