{c}

A Lobatto IIIA method collocates at the <Lobatto quadrature> nodes, including both endpoints of the time interval. Its three-stage version has
$$
A=\begin{pmatrix}0&0&0\\5/24&1/3&-1/24\\1/6&2/3&1/6\end{pmatrix},
\qquad b=(1/6,2/3,1/6)^T,
\qquad c=(0,1/2,1)^T.
$$
The <Butcher order conditions> give order four. Its <stability function> is
$$
R(z)=\frac{1+z/2+z^2/12}{1-z/2+z^2/12},
$$
which is <A-stable> but not <L-stable>. It is not <algebraically stable>: the first diagonal entry of the defining <matrix> is $2b_1a_{11}-b_1^2=-1/36$. This distinguishes linear <A-stability> from nonlinear <algebraic stability>.


 Lobatto IIIA method (source code)