Numerical solution of nonlinear integro-differential equations

Shodmonova, G; Islomov, Utkir; Abdisamatov, Otabek; Khikmatullaev, Sanjar; Kholiyorov, Umirzok; Shakhnoza, Khamraeva

doi:10.1088/1757-899x/896/1/012117

Cited by 23 publications

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“…here  is the required accuracy of the solution, S is the number of iterations, while the initial iterative value is chosen equal to the solution at the previous time level [24,25].…”

Section: Resultsmentioning

confidence: 99%

Nonlinear mathematical model and numerical algorithm for monitoring and predicting the concentration of harmful substances in the atmosphere

et al. 2021

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The article developed a nonlinear mathematical model and an effective numerical algorithm for monitoring and forecasting the process of spreading industrial emissions in the atmosphere, taking into account the orography of the area and the speed of movement of fine substances. Multidimensional partial differential equations describe the model with corresponding initial, internal, and boundary conditions of the third kind to consider mass transfer across the interface. In the work, to prove the adequacy of the developed mathematical apparatus, the calculated data are compared with field data taken from a specific object, in which the computational algorithm provides sufficient accuracy of the solution, based on which it can be concluded that the developed mathematical model and the numerical algorithm have a certain advantage over others numerical methods.

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“…here  is the required accuracy of the solution, S is the number of iterations, while the initial iterative value is chosen equal to the solution at the previous time level [24,25].…”

Section: Resultsmentioning

confidence: 99%

Nonlinear mathematical model and numerical algorithm for monitoring and predicting the concentration of harmful substances in the atmosphere

et al. 2021

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“…It provides a convenient basis, for example, for extending the statistical particle method to turbulence problems. Many scientists have worked on this topic [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Perhaps such a description will be useful for the kinetic theory of turbulence.…”

Section: Methodsmentioning

confidence: 99%

Transfer equation for the strain rate tensor and description of an incompressible dispersed mixture (incompressible fluid) by a system of equations of dynamic type

et al. 2021

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It is known that the application of the vector operation rot to the equations of hydrodynamics leads to the Helmholtz-Friedman equation for a vortex. A dispersed mixture, tensor transformations are used, in a certain sense generalizing the vector operation rot, which gives more than one, a couple of equations. One of them describes the transfer of vorticity is the well-known Helmholtz-Friedman equation. The second equation was obtained for the first time, and it describes the transfer of the strain rate tensor. Any tensor decomposes into symmetric and antisymmetric parts. By definition, the symmetric part of the tensor U is the strain rate tensor. The antisymmetric part of U is a tensor whose components are related in a known manner to the pseudovector angular velocity.

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“…where ℎ 0 ( )is the optimal estimate of the weight function of the object by criterion (10). The solution of this equation can be found by the methods described in [7,23].…”

Section: ′′ =mentioning

confidence: 99%

“…Where m is the number of subsystems allocated when building an integrated macro model; -coefficient associated with the structural properties of the system [10].…”

Section: Introductionmentioning

confidence: 99%

“…The essence of the proposed algorithm for choosing the preferred process model with regard to technological situations is as follows. If the values of the variables of the object with the definition number , = 1, in the control cycle, P then when they are substituted in (10), respectively, each model with different accuracy determines the values of the output indicator. In this case, the substitution of the values of these variables in the model of type ( 10) is carried out taking ( −1 , ).into account their affiliation to the interval.…”

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Multi-step concept of the process of building a macromode

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Building a macro and micro model of a multistage process is considered using the decomposition method, dividing the general technological system into interconnected control loops. A procedure for constructing an integrated macro model of a multistage process using a system of material balance equations for each control loop, a two-level mathematical model of a complex multistage system, developing principles for modeling and systematizing element models, the degree of aggregation, in general, controlling the technological properties of a material resource, calculating the schemes is reduced to solving a system of algebraic equations, modern technological scheme processing of a material resource, the procedure for constructing an integrated macro model multistage process (SME). A modern technological scheme for processing material resources cannot be carried out without returning circulating products when the product from subsequent nodes is sent for revision to the head of the technological scheme. The procedure for constructing an integrated macro model of SME s at two stages is considered. The task is to find the optimal solutions to the original mathematical model by interconnecting conditionally - optimal solutions of individual models. A comparison of various formal decomposition methods is performed according to previously determined criteria, and on this basis, the most preferable is chosen. When modeling multidimensional systems, one has to operate with various factors that have different units of measurement. Therefore, it is advisable to determine the dimensionless mathematical model since it is easily analyzed. The use of the latest mathematical modeling tools and modern methods of the flexible equation mainly determines the prospects of such studies.

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Numerical solution of nonlinear integro-differential equations

Cited by 23 publications

References 0 publications

Nonlinear mathematical model and numerical algorithm for monitoring and predicting the concentration of harmful substances in the atmosphere

Nonlinear mathematical model and numerical algorithm for monitoring and predicting the concentration of harmful substances in the atmosphere

Transfer equation for the strain rate tensor and description of an incompressible dispersed mixture (incompressible fluid) by a system of equations of dynamic type

Multi-step concept of the process of building a macromode

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