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Adaptive Stepsize Control
Up to now, have assumed stepsize h is constant.
Clearly prefer choosing h small when f ' is large, and h large when f ' is small.
The tradeoff is extra trial steps to determine optimum h, but may achieve factor of 10 to 100 increase in stepsize, so it's often worth it.
NRiC provides a routine odeint() for RK4 with adapative stepsize control. Complicated to use!