Poincare–tricomi Problem for the Equation of a Mixed Elliptico-Hyperbolic Type of Second Kind

Abdullayev, Akmaljon Abdujalilovich; Ergashev, Tuhtasin

doi:10.17223/19988621/65/1

Cited by 15 publications

(4 citation statements)

References 1 publication

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“…The difference of the value from zero gives reason to believe that there is a significant autocorrelation between the yield of cotton. Consequently, the yield of cotton in the Bukhara region this year depends on the yield of past years 𝑅 𝐿 [8][9][10][11][12][13][14][15]. Based on sample data, using the x7.2019 program package and Excel computer, the numerical characteristics of the average cotton yield -𝑦 𝑡 in the Bukhara region are calculated (Table 4):…”

Section: Discussionmentioning

confidence: 99%

Statistical analysis and forecasting of cotton yield dynamics in Bukhara region

Vakhabov,

Fayziev

2023

E3S Web of Conf.

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Observations on some phenomena, the nature of which changes in time, are ordered sequences, which is called the time series. In the article, by the method of statistical analysis of time series, the statistical regularity of the series of dynamics of the average yield of cotton in the Bukhara region, the Republic of Uzbekistan (based on the materials of the CSO of the Republic of Uzbekistan for 2001-2019) was studied. Point and interval estimates for the average cotton yield were built with a 95% guarantee, explicit types of trends were determined, and yields in the region were predicted for subsequent years. With the help of Durbin-Watson statistical criteria, it was found that the average cotton yield in the region has an autocorrelation dependence.

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Section: Discussionmentioning

confidence: 99%

Statistical analysis and forecasting of cotton yield dynamics in Bukhara region

Vakhabov,

Fayziev

2023

E3S Web of Conf.

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“…The class of problems to be solved can be expanded using the results obtained in [17][18][19], related to the mixed boundary conditions of the first and second kinds on the first coordinate.…”

Section: Discussionmentioning

confidence: 99%

Exact method to solve of linear heat transfer problems

2021

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When approximating multidimensional partial differential equations, the values of the grid functions from neighboring layers are taken from the previous time layer or approximation. As a result, along with the approximation discrepancy, an additional discrepancy of the numerical solution is formed. To reduce this discrepancy when solving a stationary elliptic equation, parabolization is carried out, and the resulting equation is solved by the method of successive approximations. This discrepancy is eliminated in the approximate analytical method proposed below for solving two-dimensional equations of parabolic and elliptic types, and an exact solution of the system of finite difference equations for a fixed time is obtained. To solve problems with a boundary condition of the first kind on the first coordinate and arbitrary combinations of the first, second and third kinds of boundary conditions on the second coordinate, it is proposed to use the method of straight lines on the first coordinate and ordinary sweep method on the second coordinate. Approximating the equations on the first coordinate, a matrix equation is built relative to the grid functions. Using eigenvalues and vectors of the three-diagonal transition matrix, linear combinations of grid functions are compiled, where the coefficients are the elements of the eigenvectors of the three-diagonal transition matrix. Boundary conditions, and for a parabolic equation, initial conditions are formed for a given combination of grid functions. The resulting one-dimensional differential-difference equations are solved by the ordinary sweep method. From the resulting solution, proceed to the initial grid functions. The method provides a second order of approximation accuracy on coordinates. And the approximation accuracy in time when solving the parabolic equation can be increased to the second order using the central difference in time. The method is used to solve heat transfer problems when the boundary conditions are expressed by smooth and discontinuous functions of a stationary and non-stationary nature, and the right-hand side of the equation represents a moving source or outflow of heat.

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“…Therefore, the study of non-local boundary value problems with a conormal derivative for equations of mixed elliptic-hyperbolic type of the second kindseems to be very relevant and little studied. Note the works [14,15]. In this paper, we study a nonlocal boundary value problem with the Poincaré condition for an elliptichyperbolic type equation of the second kind, i.e.…”

Section: Introductionmentioning

confidence: 99%

On the unique solvability of a nonlocal boundary value problem with the poincaré condition

2023

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As is known, it is customary in the literature to divide degenerate equations of mixed type into equations of the first and second kind. In the case of an equation of the second kind, in contrast to the first, the degeneracy line is simultaneously the envelope of a family of characteristics, i.e. is itself a characteristic, which causes additional difficulties in the study of boundary value problems for equations of the second kind. In this paper, in order to establish the unique solvability of one nonlocal problem with the Poincaré condition for an elliptic-hyperbolic equation of the second kind developed a new principle extremum, which helps to prove the uniqueness of resolutions as signed problem. The existence of a solution is realized by reducing the problem posed to a singular integral equation of normal type, which known by the Carleman-Vekua regularization method developed by S.G. Mikhlin and M.M. Smirnov equivalently reduces to the Fredholm integral equation of the second kind, and the solvability of the latter follows from the uniqueness of the solution delivered problem.

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Poincare–tricomi Problem for the Equation of a Mixed Elliptico-Hyperbolic Type of Second Kind

Cited by 15 publications

References 1 publication

Statistical analysis and forecasting of cotton yield dynamics in Bukhara region

Statistical analysis and forecasting of cotton yield dynamics in Bukhara region

Exact method to solve of linear heat transfer problems

On the unique solvability of a nonlocal boundary value problem with the poincaré condition

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