Second Derivative Multistep Methods for Stiff Ordinary Differential Equations

The difficulty associated with the numerical solution of stiff ordinary differential equations is considered and the stability requirements of methods suitable for stiff equations are described. A class of second derivative formulas is developed and the stability of these formulas is investigated. These k-step $(k + 2)$nd order formulas are shown to be suitable for stiff equations for $k \leqq 7$. These formulas have been implemented in a variable order, variable-step method and some numerical results are presented.