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2 cards from this section. Quick, good the night before a test.
What does Picard's Iteration Method primarily help us with?
Think about numerical methods.
What is the starting point for the successive approximations?
Look for where we begin our iterations.
What is the purpose of Picard's Iteration Method?
Think about the context of numerical methods.
True or False: Picard's Method can be used for any type of ODE.
Consider conditions under which it is most effective.
Use Picard's Method to approximate the solution of dy/dx = x - y with y(0) = 0. Illustrate your iterations.
Pay attention to that you should integrate each new approximation.
Consider the equation dy/dx = y^2 with initial condition y(0) = 1. Apply the Picard Method to find the first three approximations.
Remember, integration is key at each step!
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