zbMATH — the first resource for mathematics

One-step method representations of linear multi-step methods for ordinary differential equations. (Russian) Zbl 0621.65066
The Nordsieck representation of multistep methods for numerical integration of initial value problems for ordinary differential equations is considered. It is shown that any linear k-step method of order k-1 (this order reduction is made to improve stability) may be formulated as a modified (1-step) Nordsieck scheme. The interconnections between the stability characteristics of both representations are also studied.
Reviewer: V.A.Velev

65L05 Numerical methods for initial value problems
65L20 Stability and convergence of numerical methods for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems, general theory