Approximation of abstract linear integrodifferential equations
Oka, Hirokazu ; Tanaka, Naoki
Studia Mathematica, Tome 141 (2000), p. 1-14 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:216754 
@article{bwmeta1.element.bwnjournal-article-smv140i1p1bwm,
     author = {Hirokazu Oka and Naoki Tanaka},
     title = {Approximation of abstract linear integrodifferential equations},
     journal = {Studia Mathematica},
     volume = {141},
     year = {2000},
     pages = {1-14},
     zbl = {0963.45013},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv140i1p1bwm}
}

Oka, Hirokazu; Tanaka, Naoki. Approximation of abstract linear integrodifferential equations. Studia Mathematica, Tome 141 (2000) pp. 1-14. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv140i1p1bwm/

[00000] [1] G. Chen and R. Grimmer, Integral equations as evolution equations, J. Differential Equations 45 (1982), 53-74. | Zbl 0449.45008

[00001] [2] R. Grimmer and J. Prüss, On linear Volterra equations in Banach spaces, Comput. Math. Appl. 11 (1985), 189-205. | Zbl 0569.45020

[00002] [3] H. Kellermann and M. Hieber, Integrated semigroups, J. Funct. Anal. 84 (1989), 160-180. | Zbl 0689.47014

[00003] [4] J. Kisyński, A proof of the Trotter-Kato theorem on approximation of semigroups, Colloq. Math. 18 (1967), 181-184. | Zbl 0152.33905

[00004] [5] T. G. Kurtz, Extensions of Trotter's operator semigroup approximation theorems, J. Funct. Anal. 3 (1969), 354-375. | Zbl 0174.18401

[00005] [6] H. Oka, Integrated resolvent operators, J. Integral Equations Appl. 7 (1995), 193-232. | Zbl 0846.45005

[00006] [7] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, Berlin, 1983.

[00007] [8] J. Prüss, Evolutionary Integral Equations and Applications, Birkhäuser, Basel, 1993.

[00008] [9] N. Tanaka, Approximation of integrated semigroups by ``integrated'' discrete parameter semigroups, Semigroup Forum 55 (1997), 57-67. | Zbl 0897.47038

[00009] [10] V. Thomée and L. B. Wahlbin, Long-time numerical solution of a parabolic equation with memory, Math. Comp. 62 (1994), 477-496. | Zbl 0801.65135

[00010] [11] H. F. Trotter, Approximation of semigroups of operators, Pacific J. Math. 8 (1958), 887-919. | Zbl 0099.10302