A posteriori estimates of inverse operators for initial value problems in linear ordinary differential equations

We present constructive a posteriori estimates of inverse operators for initial value problems in linear ordinary differential equations (ODEs) on a bounded interval. Here, “constructive” indicates that we can obtain bounds of the operator norm in which all constants are explicitly given or are repr...

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Vydáno v:Journal of computational and applied mathematics Ročník 236; číslo 6; s. 1622 - 1636
Hlavní autoři: Kinoshita, T., Kimura, T., Nakao, M.T.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 15.10.2011
Témata:
Construction
Constructive a posteriori estimates
Differential equations
Estimates
Finite element method
Initial value problems
Inverse
Linear ODEs
Mathematical analysis
Mathematical models
Operators
65L05
Finite element method
Linear ODEs
65L70
65L60
34A30
65G99
Constructive a posteriori estimates
34L99
ISSN:0377-0427, 1879-1778
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Popis
Shrnutí:We present constructive a posteriori estimates of inverse operators for initial value problems in linear ordinary differential equations (ODEs) on a bounded interval. Here, “constructive” indicates that we can obtain bounds of the operator norm in which all constants are explicitly given or are represented in a numerically computable form. In general, it is difficult to estimate these inverse operators a priori. We, therefore, propose a technique for obtaining a posteriori estimates by using Galerkin approximation of inverse operators. This type of estimation will play an important role in the numerical verification of solutions for initial value problems in nonlinear ODEs as well as for parabolic initial boundary value problems.
Bibliografie:ObjectType-Article-2
SourceType-Scholarly Journals-1
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content type line 23
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2011.09.026