A posteriori estimates of inverse operators for initial value problems in linear ordinary differential equations |
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Authors: | T. Kinoshita T. Kimura |
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Affiliation: | a Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japanb Sasebo National College of Technology, Nagasaki 857-1193, Japan |
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Abstract: | 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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Keywords: | 34A30 34L99 65L05 65L60 65L70 65G99 |
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