Numerical Solution of Combined Inverse Problem for Generalized Burgers Equation

Gamzaev, Kh. M.

doi:10.1007/s10958-017-3271-1

Cited by 8 publications

(4 citation statements)

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“…w j+1 i , q j+1 i = 1, n, j = 0, m − 1. To solve this system, we use the approach proposed in [5]. We represent the solution of system (13) -(15) for each fixed value j in the form…”

Section: Methods For Solving the Problemmentioning

confidence: 99%

“…It is known that the direct problem for equation (1) consists in determining the function u(x, t) from equation (1) with given coefficients ν(t) > 0, λ(t), right-hand side q(t)F (x, t) and conditions (2)- (5).…”

Section: Statement Problemmentioning

confidence: 99%

“…In such problems, in addition to solving differential equations, it is required to restore the unknown parameters of external sources. Inverse problems of recovering the right-hand sides of partial differential equations of parabolic type were studied in many works [1], [2], [5], [6], [9], [11]. There is also an extensive literature on inverse problems of reconstructing the right-hand sides of wave equations [4], [7], [8], [9].…”

Section: Introductionmentioning

confidence: 99%

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Inverse Problem for Reconstructing the Right Side of a One-Dimensional Wave Equation

2022

BMJ

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An inverse problem of recovering the unknown parameter of an external source for a one-dimensional wave equation with a nonlocal additional condition is considered. It is assumed that the unknown source parameter depends only on time. By integration, the problem is transformed to an inverse boundary value problem with local conditions. A difference analogue of the differential problem in the form of an implicit difference scheme is constructed and a non-iterative computational algorithm for solving the resulting system of difference equations is proposed. As a result, an explicit formula is obtained for determining the approximate value of the sought parameter for each discrete value of the time variable

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“…w j+1 i , q j+1 i = 1, n, j = 0, m − 1. To solve this system, we use the approach proposed in [5]. We represent the solution of system (13) -(15) for each fixed value j in the form…”

Section: Methods For Solving the Problemmentioning

confidence: 99%

Section: Statement Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Inverse Problem for Reconstructing the Right Side of a One-Dimensional Wave Equation

2022

BMJ

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“…The objective relates to the class of inverse problems, which are related to the reconstruction of the right parts of the differential equations with the partial derivatives [4 -5]. Statement issues and numerical methods for the solution of inverse problems for the reconstruction of the right parts of differential equations with the partial derivatives are investigated in [4][5][6][7][8][9][10].…”

Section: Statement Of the Problem And Solution Methodsmentioning

confidence: 99%

Parallel Numerical Method of an Inverse Problem of Double-Phased Filtration

Алиев

Hamzaev²,

İsmayılova

et al. 2019

AzJHPC

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Was investigated the process of the displacement of oil with water in the horizontally located two-dimensional layer, which is described with the double-phased filtration model of incompressible liquid in non-deformable porous media. Within this model was set inverse problem for the definition flow rate of exploitative wells. Meanwhile, as additional conditions are set downhole pressure in injection wells. For the numerical solution of the problem, firstly was conducted discretization by time. As a result original problem comes down to two independent problems which are solved sequentially in each layer of time: the inverse problem for the definition of pressure distribution and flow rate of exploitative wells and forward problem for the definition of saturation of displacing phase. For the solution of the forward problem was offered particular fission, which gives an opportunity parallelization of received differential problems. In the base of the offered numerical method were carried out experimental results for model tasks. For parallelization of computing, processes was applied Open MP technology.

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