ArticleOriginal scientific text
Title
Approximation of abstract linear integrodifferential equations
Authors 1, 2
Affiliations
- Faculty of Engineering, Ibaraki University, Hitachi 316, Japan
- Department of Mathematics, Faculty of Science, Okayama University, Okayama 700, Japan
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.
Keywords
approximation of integrodifferential equation, approximation of, Banach space, resolvent operator, semigroup of class
Bibliography
- G. Chen and R. Grimmer, Integral equations as evolution equations, J. Differential Equations 45 (1982), 53-74.
- R. Grimmer and J. Prüss, On linear Volterra equations in Banach spaces, Comput. Math. Appl. 11 (1985), 189-205.
- H. Kellermann and M. Hieber, Integrated semigroups, J. Funct. Anal. 84 (1989), 160-180.
- J. Kisyński, A proof of the Trotter-Kato theorem on approximation of semigroups, Colloq. Math. 18 (1967), 181-184.
- T. G. Kurtz, Extensions of Trotter's operator semigroup approximation theorems, J. Funct. Anal. 3 (1969), 354-375.
- H. Oka, Integrated resolvent operators, J. Integral Equations Appl. 7 (1995), 193-232.
- A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, Berlin, 1983.
- J. Prüss, Evolutionary Integral Equations and Applications, Birkhäuser, Basel, 1993.
- N. Tanaka, Approximation of integrated semigroups by ``integrated'' discrete parameter semigroups, Semigroup Forum 55 (1997), 57-67.
- V. Thomée and L. B. Wahlbin, Long-time numerical solution of a parabolic equation with memory, Math. Comp. 62 (1994), 477-496.
- H. F. Trotter, Approximation of semigroups of operators, Pacific J. Math. 8 (1958), 887-919.
Pages:
1-14
Main language of publication
English
Received
1998-03-02
Accepted
1998-09-20
Published
2000
Exact and natural sciences