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  "body": "\n## Summary\n\nAdaptive step size control lets a [[numerical method for an ordinary differential equation|558XADG64M]] change its step length as it goes.\nAt each step the method estimates its [[local truncation error|T220HF0562]] and compares it with a tolerance given by the user.\nSteps whose error estimate is too large are rejected and repeated with a smaller step.\nThe next step size is predicted from the current estimate.\nIn this way the method takes long steps where the solution is smooth and short steps where it changes fast.\nIt reaches a target accuracy with far fewer steps than a fixed step size.\n\n## Explanations\n\n### L1 human\n\nThink of driving a car along a winding road: on straight parts you go fast, and before sharp bends you slow down.\nAn adaptive solver does the same with its time step.\nFor an orbit of a comet, it takes tiny steps when the comet sweeps close to the sun and very large steps far away, where little happens.\nThe error estimate plays the role of the driver's eyes.\n",
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