Backward Euler type methods for parabolic integro-differential equations in Banach space

N. Yu. Bakaev; S. Larsson; V. Thomée

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1998)

  • Volume: 32, Issue: 1, page 85-99
  • ISSN: 0764-583X

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Bakaev, N. Yu., Larsson, S., and Thomée, V.. "Backward Euler type methods for parabolic integro-differential equations in Banach space." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 32.1 (1998): 85-99. <http://eudml.org/doc/193868>.

@article{Bakaev1998,
author = {Bakaev, N. Yu., Larsson, S., Thomée, V.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {parabolic integro-differential equations; quadrature method; time discretization; Banach space; error estimates; stability; initial value problem; backward Euler type methods; parabolic equation with memory; finite element},
language = {eng},
number = {1},
pages = {85-99},
publisher = {Dunod},
title = {Backward Euler type methods for parabolic integro-differential equations in Banach space},
url = {http://eudml.org/doc/193868},
volume = {32},
year = {1998},
}

TY - JOUR
AU - Bakaev, N. Yu.
AU - Larsson, S.
AU - Thomée, V.
TI - Backward Euler type methods for parabolic integro-differential equations in Banach space
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1998
PB - Dunod
VL - 32
IS - 1
SP - 85
EP - 99
LA - eng
KW - parabolic integro-differential equations; quadrature method; time discretization; Banach space; error estimates; stability; initial value problem; backward Euler type methods; parabolic equation with memory; finite element
UR - http://eudml.org/doc/193868
ER -

References

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  1. [1] M. CROUZEIX, S. LARSSON and V. THOMÉE, Resolvent estimates for elliptic finite element operators in one dimension, Math. Comp. 63 (1994), 121-140. Zbl0806.65096MR1242058
  2. [2] A. PAZY, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, Berlin and New York, 1983. Zbl0516.47023MR710486
  3. [3] A. H. SCHATZ, V. THOMÉE and L. B. WAHLBIN, Maximum norm stability and error estimates in parabolic finite element equations, Comm. Pure Appl. Math. 33 (1980), 265-304. Zbl0414.65066MR562737
  4. [4] I. H. SLOAN and V. THOMÉE, Time discretization of an integro-differential equation of parabolic type, SIAM J. Numer. Anal. 23 (1986), 1052-1061. Zbl0608.65096MR859017
  5. [5] V. THOMÉE and N.-Y. ZHANG, Error estimates for semidiscrete finite element methods for parabolic integro-differential equations, Math. Comp. 53 (1989). 121-139. Zbl0673.65099MR969493
  6. [6] N.-Y. ZHANG, On fully discrete Galerkin approximations for partial integro-differential equations of parabolic type, Math. Comp. 60 (1993), 133-166. Zbl0795.65098MR1149295

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