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