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Game Cards — Chapter 10
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IVP
An initial-value problem advances from initial data using a time-stepping method.
Local/global error
Local error is one-step; global error is accumulated and controlled by stability.
Stability region
Apply the method to \(y'=\lambda y\) to study step-size stability.
Adaptive control
Adaptive solvers use an error estimator to choose the next step size.
Runge--Kutta
Runge--Kutta methods combine stage slopes to achieve higher accuracy without multistep history.
Euler
Euler's method is first order and illustrates consistency and stability but is rarely enough for production.