The Numerical Algorithms for the Measurement of the Deterministic and Stochastic Signals

Keller, A.V.; Shestakov, A. L.; Sviridyuk, G. A.; Khudyakov, Yurii V.

doi:10.1007/978-3-319-12145-1_11

Cited by 27 publications

(8 citation statements)

References 8 publications

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“…Let us introduce an r × r matrix B 1 = A 2 A 1 and assume that det B 1 ̸ = 0. Then taking into account Lemma 3, the solution to (18) can be reduced to the successive solution of (7), (8), which are in this case as follows: where det B 1 ̸ = 0, u 1 (x, t) = (u 11 (x, t), . .…”

Section: The Existence and Methods Of Constructing Solutions Of Nonclmentioning

confidence: 99%

“…Sviridyuk's results from the theory of semigroups with kernels [6]. These approaches are applied to various problems [7,8].…”

Section: Introductionmentioning

confidence: 99%

“…Let us introduce two lemmas establishing the link between (6) and system 7, (8) to answer that question. Proof.…”

Section: Introduce a System Of Two Equationsmentioning

confidence: 99%

“…Proof. The element −f + A 1 Lu * 1 belongs to the range of operator L 1 , because a pair u * 1 , u * satises (7), (8). Hence…”

Section: Introduce a System Of Two Equationsmentioning

confidence: 99%

“…Suppose that a pair (u * 1 , u * ) is a solution to (7),(8). Let the operator L 1 have right inverse L −1 Then element u * satises (6).…”

mentioning

confidence: 99%

See 4 more Smart Citations

Solution of Irregular Systems of Partial Differential Equations Using Skeleton Decomposition of Linear Operators

Sidorov¹,

Sidorov²

2017

Bulletin of the SUSU. MMP

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The linear system of partial dierential equations is considered. It is assumed that there is an irreversible linear operator in the main part of the system. The operator is assumed to enjoy the skeletal decomposition. The dierential operators of such system are assumed to have suciently smooth coecients. In the concrete situations the domains of such dierential operators are linear manifolds of smooth enough functions with values in Banach space. Such functions are assumed to satisfy additional boundary conditions. The concept of a skeleton chain of linear operator is introduced. It is assumed that the operator generates a skeleton chain of the nite length. In this case, the problem of solution of a given system is reduced to a regular split system of equations. The system is resolved with respect to the highest dierential expressions taking into account certain initial and boundary conditions. The proposed approach can be generalized and applied to the boundary value problems in the nonlinear case. Presented results develop the theory of degenerate dierential equations summarized in the monographs MR 87a:58036, Zbl 1027.47001.

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Section: The Existence and Methods Of Constructing Solutions Of Nonclmentioning

confidence: 99%

“…Sviridyuk's results from the theory of semigroups with kernels [6]. These approaches are applied to various problems [7,8].…”

Section: Introductionmentioning

confidence: 99%

“…Let us introduce two lemmas establishing the link between (6) and system 7, (8) to answer that question. Proof.…”

Section: Introduce a System Of Two Equationsmentioning

confidence: 99%

“…Proof. The element −f + A 1 Lu * 1 belongs to the range of operator L 1 , because a pair u * 1 , u * satises (7), (8). Hence…”

Section: Introduce a System Of Two Equationsmentioning

confidence: 99%

“…Suppose that a pair (u * 1 , u * ) is a solution to (7),(8). Let the operator L 1 have right inverse L −1 Then element u * satises (6).…”

mentioning

confidence: 99%

See 3 more Smart Citations

Solution of Irregular Systems of Partial Differential Equations Using Skeleton Decomposition of Linear Operators

Sidorov¹,

Sidorov²

2017

Bulletin of the SUSU. MMP

View full text Add to dashboard Cite

show abstract

Optimal dynamic measurements in presence of the random interference

Shestakov

Sagadeeva

Manakova

et al. 2018

J. Phys.: Conf. Ser.

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Numerical study of the optimal control problem for one model of potential distribution in a crystalline semiconductor with the Showalter–Sidorov condition

Vasiuchkova

2021

J. Phys.: Conf. Ser.

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The paper considers a mathematical model of potentials optimal distribution in a crystalline semiconductor. This model is based on the problem of optimal control of weak generalized solutions of the mathematical model of the potential distribution in a crystalline semiconductor with the Showalter–Sidorov condition. The theoretical results obtained by us earlier made it possible to develop an algorithm for a numerical method for finding an approximate one by solutions of the optimal control problem for the problem under study, based on the methods of decomposition, Ritz, penalty and Galerkin’s projection method. The results of a computational experiment are presented.

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The Numerical Algorithms for the Measurement of the Deterministic and Stochastic Signals

Cited by 27 publications

References 8 publications

Solution of Irregular Systems of Partial Differential Equations Using Skeleton Decomposition of Linear Operators

Solution of Irregular Systems of Partial Differential Equations Using Skeleton Decomposition of Linear Operators

Optimal dynamic measurements in presence of the random interference

Numerical study of the optimal control problem for one model of potential distribution in a crystalline semiconductor with the Showalter–Sidorov condition

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