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  "body": "\n## Summary\n\nA linear multistep method solves an [[initial value problem|0FXDW992DS]] $y' = f(t, y)$ numerically.\nIt computes the next approximation from a fixed number of earlier approximations and the values of $f$ there.\nIt needs only one new evaluation of $f$ per step, which makes it cheap compared with [[Runge–Kutta methods|7DBPJKYC6C]] of the same order.\nThe Adams methods and the [[backward differentiation formulas|TDA94C2JYT]] are the main families.\nIts convergence is governed by consistency and zero-stability, and its possible order is limited by the [[Dahlquist barriers|BQBZ7QMJE2]].\n\n## Explanations\n\n### L1 human\n\nWhen you walk along a curve and have already recorded several points, you can use all of them to guess where the curve goes next.\nA linear multistep method does this: it combines the last few positions and slopes with fixed weights.\nFor example, the two-step Adams–Bashforth method steps forward by $h \\left( \\frac32 f_{k+1} - \\frac12 f_k \\right)$, an extrapolation of the last two slopes.\nThe first few values must be supplied by another method, such as a Runge–Kutta method.\n",
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