A Lobatto IIIA method collocates at the Lobatto quadrature nodes, including both endpoints of the time interval. Its three-stage version has
(1)
The Butcher order conditions give order four. Its stability function is
(2)
which is A-stable but not L-stable. It is not algebraically stable: the first diagonal entry of the defining matrix is . This distinguishes linear A-stability from nonlinear algebraic stability.

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  1. Collocation Runge-Kutta method
  2. Implicit Runge-Kutta method
  3. Runge-Kutta method
  4. Numerical analysis
  5. Analysis
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