Adaptive step size

Summary

Adaptive step size control lets a numerical method for an ordinary differential equation change its step length as it goes. At each step the method estimates its local truncation error and compares it with a tolerance given by the user. Steps whose error estimate is too large are rejected and repeated with a smaller step. The next step size is predicted from the current estimate. In this way the method takes long steps where the solution is smooth and short steps where it changes fast. It reaches a target accuracy with far fewer steps than a fixed step size.