= Fourth-order two-stage Gauss collocation method
{title2=$R(z)=(1+z/2+z^2/12)/(1-z/2+z^2/12)$}
The two-stage <Gauss--Legendre Runge-Kutta method> uses nodes $c_{1,2}=1/2\mp\sqrt3/6$, weights $b_1=b_2=1/2$ and coefficients $a_{11}=a_{22}=1/4$, $a_{12}=1/4-\sqrt3/6$, $a_{21}=1/4+\sqrt3/6$. The <Butcher order conditions> give order four. Its <stability function> is the displayed rational function, which is <A-stable>. The <algebraic stability> matrix is zero, so positive weights also give nonlinear contractivity for dissipative vector fields.
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