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  "body": "\n## Summary\n\nRichardson extrapolation combines two approximations computed with step sizes $h$ and $h/t$ so that the leading term of their error cancels.\nIt applies whenever the error of a method has a known expansion in powers of the step size.\nRepeated, it turns the trapezoidal rule into Romberg integration, and it is used throughout numerical differentiation, integration and the solution of differential equations.\n\n## Explanations\n\n### L1 human\n\nSuppose a method has error roughly proportional to $h^2$, where $h$ is a step size.\nHalving $h$ divides the error by about $4$.\nKnowing this, one can combine the two results so that the $h^2$ parts cancel exactly: $\\frac{4 A(h/2) - A(h)}{3}$.\nWhat remains is a much smaller error, of higher order in $h$.\n",
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