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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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 236; no. 6; pp. 1622 - 1636
Main Authors: Kinoshita, T., Kimura, T., Nakao, M.T.
Format: Journal Article
Language:English
Published: Elsevier B.V 15.10.2011
Subjects:
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
Online Access:Get full text
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Summary: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.
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content type line 23
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2011.09.026