Abstract
This paper presents a computer-assisted procedure to prove the invertibility of a linear operator which is the sum of an unbounded bijective and a bounded operator in a Hilbert space, and to compute a bound for the norm of its inverse. By using some projection and constructive a priori error estimates, the invertibility condition together with the norm computation is formulated as an inequality based upon a method originally developed by the authors for obtaining existence and enclosure results for nonlinear partial differential equations. Several examples which confirm the actual effectiveness of the procedure are reported.
Original language | English |
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Pages (from-to) | 6363-6374 |
Number of pages | 12 |
Journal | Journal of Differential Equations |
Volume | 260 |
Issue number | 7 |
DOIs | |
Publication status | Published - 2016 Apr 5 |
Externally published | Yes |
Keywords
- Differential operators
- Numerical verification
- Solvability of linear problem
ASJC Scopus subject areas
- Analysis