Optimal Difference Formulas in the Sobolev Space
- Authors: Shadimetov K.M.1, Mirzakabilov R.N.2
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Affiliations:
- Tashkent State Transport University
- Romanovskiy Institute of Mathematics
- Issue: Vol 68, No 1 (2022): Science — Technology — Education — Mathematics — Medicine
- Pages: 167-177
- Section: Articles
- URL: https://journals.rudn.ru/CMFD/article/view/30859
- DOI: https://doi.org/10.22363/2413-3639-2022-68-1-167-177
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Abstract
Optimization of computational methods in functional spaces is one of the main problems of computational mathematics. In this paper, algebraic and functional assertions for the problem of difference formulas are discussed. For optimization of difference formulas, i.e., for construction of optimal difference formulas in functional spaces, an important role is played by the extremal function of the given difference formula. In this work, we explicitly find in Sobolev spaces the extremal function of the difference formula and compute the norm of the error functional of the difference formula. Furthermore, we prove existence and uniqueness of the optimal difference formula.
About the authors
Kh. M. Shadimetov
Tashkent State Transport University
Author for correspondence.
Email: kholmatshadimetov@mail.ru
Tashkent, Uzbekistan
R. N. Mirzakabilov
Romanovskiy Institute of Mathematics
Email: ravshan.m.n@mail.ru
Tashkent, Uzbekistan
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