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. 

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