Exact method to solve finite difference equations of linear heat transfer problems

Abdullayev, Akmaljon Abdujalilovich; Hidoyatova, Muyassar

doi:10.1063/5.0071430

Cited by 7 publications

(2 citation statements)

References 6 publications

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“…Therefore, the study of boundary value problems for mixed-type equations of the second kind seems very relevant and little studied. We note the works [3][4][5][6].…”

Section: Introductionmentioning

confidence: 99%

About one boundary-value problem arising in modeling dynamics of groundwater

2023

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Modeling the movement of moisture in the soil is of great importance for assessing the impact of agricultural land on surface water bodies and, consequently, on the natural environment and humans. This is because huge volumes of pollutants from the fields (pesticides, mineral fertilizers, nitrates, and nutrients contained in them) are transferred to reservoirs by filtering moisture. Different methods solve all these tasks. The method of natural analogies is based on the analysis of graphs of fluctuations in groundwater level. To apply this method on irrigated lands, it is necessary to have a sufficiently studied irrigated area with similar natural, organizational and economic conditions. The successful application of this method, based on the fundamental theory of physical similarity, mainly depends on the availability of a sufficiently close comparison object, which is quite rare in practice. Physical modeling is often used to construct dams and other hydraulic structures. Previously, the method of electrical modeling was also widely used. It was further found that nonlocal boundary conditions arise in the problems of predicting soil moisture, modeling fluid filtration in porous media, mathematical modeling of laser radiation processes, and plasma physics problems, as well as mathematical biology.

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“…Therefore, the study of boundary value problems for mixed-type equations of the second kind seems very relevant and little studied. We note the works [3][4][5][6].…”

Section: Introductionmentioning

confidence: 99%

About one boundary-value problem arising in modeling dynamics of groundwater

2023

Self Cite

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“…In general, the time series consists of four components: trend; fluctuations relative to the trend; seasonality effect; random component. The following works are devoted to the study and analysis of dynamic series: Anderson, Kendal, Brillinger, Chetyrkin, Vain, Sulaimanov {𝑦 𝑡 , 𝑡 ∈ 𝑇} [1][2][3][4][5][6][7] other. The study of the yield of agricultural processes, as a discrete dynamic series and forecasting their yield based on experimental data, play an important role in determining the economic efficiency of farming and dekhkan farms.…”

Section: Introductionmentioning

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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About one differential model of dynamics of groundwater

Abdullayev,

Hidoyatova,

Kuralov

2023

E3S Web of Conf.

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When modeling the flow of groundwater and streams together, two different approaches are used, using hydraulic and hydrological models as channel flow models. The former is based on mathematical equations of water movement in open channels. In contrast, the latter is based on simplified empirical and semi-empirical relationships between the hydraulic characteristics of watercourses. In both cases, the watercourse is an internal boundary for the groundwater flow - otherwise, it is advisable to model it as a body of water. The groundwater model can be a scale model or an electrical model of the state of the groundwater or an aquifer. Groundwater models are used to represent the natural flow of groundwater in an environment. Some groundwater models include aspects of groundwater quality. Such groundwater models attempt to predict the fate and movement of a chemical in natural, urban, or hypothetical scenarios. Groundwater models can be used to predict the impact of hydrological changes on aquifer behavior and are often referred to as groundwater simulation models. Also, groundwater models are currently being used in various water management plans for urban areas. Because calculations in mathematical groundwater models are based on groundwater flow equations, which are differential equations that can often only be solved by approximate methods using numerical analysis, these models are also referred to as mathematical, numerical, or computational groundwater models.

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Exact method to solve finite difference equations of linear heat transfer problems

Cited by 7 publications

References 6 publications

About one boundary-value problem arising in modeling dynamics of groundwater

About one boundary-value problem arising in modeling dynamics of groundwater

Statistical analysis and forecasting of cotton yield dynamics in Bukhara region

About one differential model of dynamics of groundwater

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