On the stability of variable-stepsize Nordsieck BDF methods
SIAM Journal on Numerical Analysis
On the stability of interpolatory variable-stepsize Adams methods in Nordsieck form
SIAM Journal on Numerical Analysis
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
SIAM Journal on Numerical Analysis
A Polyalgorithm for the Numerical Solution of Ordinary Differential Equations
ACM Transactions on Mathematical Software (TOMS)
On quasi-consistent integration by Nordsieck methods
Journal of Computational and Applied Mathematics
Variable-Stepsize Interpolating Explicit Parallel Peer Methods with Inherent Global Error Control
SIAM Journal on Scientific Computing
Global Error Control in Adaptive Nordsieck Methods
SIAM Journal on Scientific Computing
Local and global error estimation and control within explicit two-step peer triples
Journal of Computational and Applied Mathematics
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In this paper we study an order reduction phenomenon arising in Nordsieck methods when they are applied to ordinary differential equations on nonuniform grids. It causes some difficulties of using stepsize selection strategies in practical computations. We prove that the problem mentioned above is just a consequence of the fact that the concepts of consistency and quasi-consistency are not equivalent for such methods. The paper is also supplied with numerical examples which clearly confirm the presented theory.