- Mathematics
- Published 1977
DOI:10.1007/bf01404346

# On the behaviour of global errors at infinity in the numerical integration of stable initial value problems

@article{Nevanlinna1977OnTB, title={On the behaviour of global errors at infinity in the numerical integration of stable initial value problems}, author={O. Nevanlinna}, journal={Numerische Mathematik}, year={1977}, volume={28}, pages={445-454} }

SummaryWe consider the numerical solution of the nonlinear initial value problem
$$x' + g\left( x \right) = f\left( t \right), t > 0, x\left( 0 \right) = c \in R^n $$
by some linear multistep methods. We show that ifg is monotone andx(t) is smooth enough at infinity, then the global error tends to a trigonometric polynomial asn h → ∞ with step sizeh fixed. Often the trigonometric polynomial vanishes identically.

#### Citations

##### Publications citing this paper.

SHOWING 1-3 OF 3 CITATIONS

## The Z-transform and linear multistep stability ∗

VIEW 19 EXCERPTS

CITES BACKGROUND, METHODS & RESULTS

HIGHLY INFLUENCED

## A Lyapunov exponents based stability theory for ODE initial value problem solvers

VIEW 1 EXCERPT

CITES RESULTS

## Exponential stability of time-varying linear systems Preprint

VIEW 1 EXCERPT

CITES METHODS