# Approximation of abstract linear integrodifferential equations

Studia Mathematica (2000)

- Volume: 140, Issue: 1, page 1-14
- ISSN: 0039-3223

## Access Full Article

top## Abstract

top## How to cite

topOka, Hirokazu, and Tanaka, Naoki. "Approximation of abstract linear integrodifferential equations." Studia Mathematica 140.1 (2000): 1-14. <http://eudml.org/doc/216754>.

@article{Oka2000,

abstract = {This paper is devoted to the approximation of abstract linear integrodifferential equations by finite difference equations. The result obtained here is applied to the problem of convergence of the backward Euler type discrete scheme.},

author = {Oka, Hirokazu, Tanaka, Naoki},

journal = {Studia Mathematica},

keywords = {approximation of integrodifferential equation; approximation of; Banach space; resolvent operator; semigroup of class $(C_0)$; linear operators; Cauchy problem; finite differences; abstract linear integrodifferential equations},

language = {eng},

number = {1},

pages = {1-14},

title = {Approximation of abstract linear integrodifferential equations},

url = {http://eudml.org/doc/216754},

volume = {140},

year = {2000},

}

TY - JOUR

AU - Oka, Hirokazu

AU - Tanaka, Naoki

TI - Approximation of abstract linear integrodifferential equations

JO - Studia Mathematica

PY - 2000

VL - 140

IS - 1

SP - 1

EP - 14

AB - This paper is devoted to the approximation of abstract linear integrodifferential equations by finite difference equations. The result obtained here is applied to the problem of convergence of the backward Euler type discrete scheme.

LA - eng

KW - approximation of integrodifferential equation; approximation of; Banach space; resolvent operator; semigroup of class $(C_0)$; linear operators; Cauchy problem; finite differences; abstract linear integrodifferential equations

UR - http://eudml.org/doc/216754

ER -

## References

top- [1] G. Chen and R. Grimmer, Integral equations as evolution equations, J. Differential Equations 45 (1982), 53-74. Zbl0449.45008
- [2] R. Grimmer and J. Prüss, On linear Volterra equations in Banach spaces, Comput. Math. Appl. 11 (1985), 189-205. Zbl0569.45020
- [3] H. Kellermann and M. Hieber, Integrated semigroups, J. Funct. Anal. 84 (1989), 160-180. Zbl0689.47014
- [4] J. Kisyński, A proof of the Trotter-Kato theorem on approximation of semigroups, Colloq. Math. 18 (1967), 181-184. Zbl0152.33905
- [5] T. G. Kurtz, Extensions of Trotter's operator semigroup approximation theorems, J. Funct. Anal. 3 (1969), 354-375. Zbl0174.18401
- [6] H. Oka, Integrated resolvent operators, J. Integral Equations Appl. 7 (1995), 193-232. Zbl0846.45005
- [7] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, Berlin, 1983.
- [8] J. Prüss, Evolutionary Integral Equations and Applications, Birkhäuser, Basel, 1993.
- [9] N. Tanaka, Approximation of integrated semigroups by ``integrated'' discrete parameter semigroups, Semigroup Forum 55 (1997), 57-67. Zbl0897.47038
- [10] V. Thomée and L. B. Wahlbin, Long-time numerical solution of a parabolic equation with memory, Math. Comp. 62 (1994), 477-496. Zbl0801.65135
- [11] H. F. Trotter, Approximation of semigroups of operators, Pacific J. Math. 8 (1958), 887-919. Zbl0099.10302

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.