One-leg variable-coefficient formulas for ordinary differential equations and local-global step size control (Q857860)

This paper is concerned with the numerical solution of initial value problems for differential systems by means of the so called one-leg linear multistep methods introduced by \textit{G. Dahlquist} [Lect. Notes Math. 506, 60--72 (1976; Zbl 0352.65042)]. Here the authors consider zero stable methods on nonuniform grids proving the existence of methods up to order 11 and giving explicitly their coefficients for second and third order methods. In addition, local and global error estimation techniques are proposed following the ideas developed the ideas used by authors in some previous papers for linear multistep methods.