One-step method representations of linear multi-step methods for ordinary differential equations. (Russian) Zbl 0621.65066

Gerasimov, B. P.; Kul’chitskaya, I. A.

Zh. Vychisl. Mat. Mat. Fiz. 27, No. 1, 76-82 (1987).

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

MSC:

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

Keywords:

Nordsieck method; multistep methods; order reduction; stability