NDLI: On the informative power of all possible linear functionals for the discretization of solutions of the Klein-Gordon equation in the metric of L 2,∞

Content Provider	Springer Nature Link
Author	Ibatulin, I. Zh. Temirgaliev, N.
Copyright Year	2008
Abstract	For the Klein-Gordon equation with initial conditions in Nikol’skii classes, we obtain sharp orders of discretization errors with respect to precise information. In particular, these orders imply qualitatively and quantitatively that raising the smoothness of one of the initial conditions relative to the other does not improve the discretization characteristics of the solution of the equation. Bounds for information distortion are given under which the limit possible errors, i.e., discretization errors with respect to precise information, are still maintained. This is important because superfluous computational accuracy used when implementing an algorithm results in an unjustified increase in memory requirements and the number of arithmetic operations without improving the accuracy inherent to the algorithm. The quality of approximation aggregates is also estimated in mean square with respect to probability measures on Nikol’skii classes.
Starting Page	510
Ending Page	526
Page Count	17
File Format	PDF
ISSN	00122661
Journal	Differential Equations
Volume Number	44
Issue Number	4
e-ISSN	16083083
Language	English
Publisher	SP MAIK Nauka/Interperiodica
Publisher Date	2008-07-22
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Difference and Functional Equations Partial Differential Equations Ordinary Differential Equations
Content Type	Text
Resource Type	Article
Subject	Analysis

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