= First Dahlquist barrier
For a consistent <zero-stable> real linear $k$-step method with constant coefficients and only first-derivative evaluations, the attainable order is at most $k+1$ for odd $k$ and $k+2$ for even $k$. For an explicit method the bound is $k$. These are order barriers under the <root condition for a multistep method>, not bounds on multiderivative methods or on arbitrary variable-step formulations. The <Second Dahlquist barrier> adds the stronger bound of order two for irreducible <A-stable> methods.
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