Construction of optimal interpolation formula exact for trigonometric functions by Sobolev’s method
Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2022 The paper is devoted to derivation of the optimal interpolation formula in W2(0,2)(0,1) Hilbert space by Sobolev’s method. Here the interpolation formula consists of a linear combination ΣNβ=0Cβφ(xβ) of the given values of a function φ from the space ...
Shadimetov, Kh.M. +2 more
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IDENTIFICATION OF THE RIGHT HAND SIDE OF A QUASILINEAR PSEUDOPARABOLIC EQUATION WITH MEMORY TERM
Вестник КазНУ. Серия математика, механика, информатика, 2021 The study of equations of mathematical physics, including inverse problems, is relevant today. This work is devoted to the fundamental problem of studying the solvability and qualitative properties of the solution of the inverse problem for a ...
S. E. Aitzhanov +2 more
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Optimal quadrature formulas for oscillatory integrals in the Sobolev space
Journal of Inequalities and Applications, 2022 This work studies the problem of construction of optimal quadrature formulas in the sense of Sard in the space L 2 ( m ) ( 0 , 1 ) $L_{2}^{(m)}(0,1)$ for numerical calculation of Fourier coefficients. Using Sobolev’s method, we obtain new sine and cosine
Kholmat Shadimetov +2 more
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An exponential-trigonometric spline minimizing a seminorm in a Hilbert space
Advances in Difference Equations, 2020 In the present paper, using the discrete analogue of the operator d 6 / d x 6 − 1 $\mathrm{d} ^{6}/\mathrm{d} x^{6}-1$ , we construct an interpolation spline that minimizes the quantity ∫ 0 1 ( φ ‴ ( x ) + φ ( x ) ) 2 d x $\int _{0}^{1}(\varphi {'''}(x)+\
Kholmat M. Shadimetov, Aziz K. Boltaev
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Linear Pantographic Sheets: Existence and Uniqueness of Weak Solutions [PDF]
, 2018 The well-posedness of the boundary value problems for second gradient elasticity has been studied under the assumption of strong ellipticity of the dependence on the second placement gradients (see, e.g., Chambon and Moullet in Comput. Methods Appl. Mech.
Boutin, Claude +3 more
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Quasilinear problems involving a perturbation with quadratic growth in the gradient and a noncoercive zeroth order term [PDF]
, 2015 In this paper we consider the problem u in H^1_0 (Omega), - div (A(x) Du) = H(x, u, Du) + f(x) + a_0 (x) u in D'(Omega), where Omega is an open bounded set of R^N, N \geq 3, A(x) is a coercive matrix with coefficients in L^\infty(Omega), H(x, s, xi) is a
Hamour, Boussad, Murat, François
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Convergence of the complete electromagnetic fluid system to the full compressible magnetohydrodynamic equations [PDF]
, 2015 The full compressible magnetohydrodynamic equations can be derived formally from the complete electromagnetic fluid system in some sense as the dielectric constant tends to zero.
Jiang, Song, Li, Fucai
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Accelerated finite difference schemes for stochastic partial differential equations in the whole space [PDF]
, 2010 We give sufficient conditions under which the convergence of finite difference approximations in the space variable of the solution to the Cauchy problem for linear stochastic PDEs of parabolic type can be accelerated to any given order of convergence by
Gyongy, Istvan, Krylov, Nicolai
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Continuous dependence for NLS in fractional order spaces [PDF]
, 2010 We consider the Cauchy problem for the nonlinear Schr\"odinger equation $iu_t+ \Delta u+ \lambda |u|^\alpha u=0$ in $\R^N $, in the $H^s$-subcritical and critical cases ...
Cazenave, Thierry +2 more
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Calculation of Coefficients of the Optimal Quadrature Formulas in
AxiomsIn this paper, we construct an optimal quadrature formula in the sense of Sard by Sobolev’s method in the W2(7,0) space. We give explicit expressions for the corresponding optimal coefficients.
Ying Yang, Xuehua Li
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