= A-stable third-order two-step multiderivative method
{c}
{title2=$7y_{n+2}-6hy'_{n+2}+2h^2y''_{n+2}=8y_{n+1}-y_n$}
The endpoint expansion of this <multiderivative multistep method> has unscaled defect $h^4y^{(4)}/3+O(h^5)$ and <zero-stability> roots $1,1/7$, giving third-order convergence with suitably accurate starting values. On the <Dahlquist test equation> its amplification roots obey $(7-6z+2z^2)\zeta^2-8\zeta+1=0$. The <complex quadratic Schur criterion> puts both roots in the open unit disk for $\operatorname{Re}z<0$, and only the simple root one reaches the boundary at $z=0$. Thus it is <A-stable>; its higher derivative places it outside the hypotheses of the <Second Dahlquist barrier>.
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