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==First and second Dahlquist barriers==
These two results were proved by [[Germund Dahlquist]] and represent an important bound for the order of convergence and for the A-stability of a linear multistep method. The first Dahlquist barrier was proved in {{harvtxt|Dahlquist|1956}} and the second in {{harvtxt|Dahlquist|1963}}.
===First Dahlquist barrier===
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===Second Dahlquist barrier===
There are no explicit A-stable and linear multistep methods. The implicit ones have order of convergence at most 2. The [[trapezoidal rule (differential equations)|trapezoidal rule]] has the smallest error constant amongst the A-stable linear multistep methods of order 2
== See also ==
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