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3 cards from this section. Quick, good the night before a test.
What is the order of accuracy for the RK4 method?
Think about how many evaluations are made.
What does RK4 stand for?
Connect the abbreviation to its full name.
What method uses four calculations for slope estimation?
Consider the number of evaluations each method employs.
True or False: The RK4 method always requires less computational effort than RK2.
Reflect on the workload involved with each method.
Given the differential equation dy/dx = sin(x) with y(0) = 0, apply the RK4 method over the interval [0, π/2] with a step size of h = 0.1. Calculate y(π/2).
Pay close attention to how the sin function behaves within this interval.
Consider the equation dy/dx = (y^2)/x with the initial condition y(1) = 1. Use RK4 to approximate y(2) using h = 0.5.
Use each k value carefully as y grows rapidly in this region.
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