Accelero-summation of the formal solutions of nonlinear difference equations

Geertrui Klara Immink[1]

  • [1] University of Groningen Faculty of Economics P.O. Box 800 9700 AV Groningen (The Netherlands)

Annales de l’institut Fourier (2011)

  • Volume: 61, Issue: 1, page 1-51
  • ISSN: 0373-0956

Abstract

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In 1996, Braaksma and Faber established the multi-summability, on suitable multi-intervals, of formal power series solutions of locally analytic, nonlinear difference equations, in the absence of “level 1 + ”. Combining their approach, which is based on the study of corresponding convolution equations, with recent results on the existence of flat (quasi-function) solutions in a particular type of domains, we prove that, under very general conditions, the formal solution is accelero-summable. Its sum is an analytic solution of the equation, represented asymptotically by the formal solution in a certain unbounded domain.

How to cite

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Immink, Geertrui Klara. "Accelero-summation of the formal solutions of nonlinear difference equations." Annales de l’institut Fourier 61.1 (2011): 1-51. <http://eudml.org/doc/219670>.

@article{Immink2011,
abstract = {In 1996, Braaksma and Faber established the multi-summability, on suitable multi-intervals, of formal power series solutions of locally analytic, nonlinear difference equations, in the absence of “level $1^+$”. Combining their approach, which is based on the study of corresponding convolution equations, with recent results on the existence of flat (quasi-function) solutions in a particular type of domains, we prove that, under very general conditions, the formal solution is accelero-summable. Its sum is an analytic solution of the equation, represented asymptotically by the formal solution in a certain unbounded domain.},
affiliation = {University of Groningen Faculty of Economics P.O. Box 800 9700 AV Groningen (The Netherlands)},
author = {Immink, Geertrui Klara},
journal = {Annales de l’institut Fourier},
keywords = {Nonlinear difference equation; formal solution; accelero-summation; quasi-function; nonlinear difference equation},
language = {eng},
number = {1},
pages = {1-51},
publisher = {Association des Annales de l’institut Fourier},
title = {Accelero-summation of the formal solutions of nonlinear difference equations},
url = {http://eudml.org/doc/219670},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Immink, Geertrui Klara
TI - Accelero-summation of the formal solutions of nonlinear difference equations
JO - Annales de l’institut Fourier
PY - 2011
PB - Association des Annales de l’institut Fourier
VL - 61
IS - 1
SP - 1
EP - 51
AB - In 1996, Braaksma and Faber established the multi-summability, on suitable multi-intervals, of formal power series solutions of locally analytic, nonlinear difference equations, in the absence of “level $1^+$”. Combining their approach, which is based on the study of corresponding convolution equations, with recent results on the existence of flat (quasi-function) solutions in a particular type of domains, we prove that, under very general conditions, the formal solution is accelero-summable. Its sum is an analytic solution of the equation, represented asymptotically by the formal solution in a certain unbounded domain.
LA - eng
KW - Nonlinear difference equation; formal solution; accelero-summation; quasi-function; nonlinear difference equation
UR - http://eudml.org/doc/219670
ER -

References

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