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  "body": "\n## Summary\n\nRunge–Kutta methods are one-step methods for the numerical solution of an [[initial value problem|0FXDW992DS]] $y' = f(t, y)$, $y(t_0) = y_0$.\nEach step evaluates $f$ at several intermediate points, the stages, and combines these slopes to advance the solution.\nThey reach high order without derivatives of $f$, and they include the [[Euler method|0JARTXX4XP]], the classical fourth-order method, and implicit methods for [[stiff equations|RR5FCG92PN]].\nA method is described by its coefficients, collected in a Butcher tableau.\n\n## Explanations\n\n### L1 human\n\nThe Euler method follows the slope at the start of each step, which is crude.\nA Runge–Kutta method first probes the slope at a few points inside the step and then takes a weighted average of them.\nThis is like checking the road ahead before deciding how to steer.\nThe classical fourth-order method uses four slopes per step; halving the step size makes its error about sixteen times smaller.\n",
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