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Optimal difference formulas in the Sobolev space
Kh. M. Shadimetova, R. N. Mirzakabilovb a Tashkent State Transport University, Tashkent, Uzbekistan
b Romanovskiy Institute of Mathematics, Tashkent, Uzbekistan
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.
Citation:
Kh. M. Shadimetov, R. N. Mirzakabilov, “Optimal difference formulas in the Sobolev space”, Science — Technology — Education — Mathematics — Medicine, CMFD, 68, no. 1, PFUR, M., 2022, 167–177
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https://www.mathnet.ru/eng/cmfd460 https://www.mathnet.ru/eng/cmfd/v68/i1/p167
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Abstract page: | 108 | Full-text PDF : | 58 | References: | 24 |
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