Кафедра математики

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Browsing Кафедра математики by Author "Drin, Iryna"

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    The analytical view of solution of the first boundary value problem for the nonlinear equation of heat conduction with deviation of the argument
    (2023) Drin, Yaroslav; Drin, Iryna; Drin, Svitlana
    In this article, for the first time, the first boundary value problem for the equation of thermal conductivity with a variable diffusion coefficient and with a nonlinear term, which depends on the sought function with the deviation of the argument, is solved. For such equations, the initial condition is set on a certain interval. Physical and technical reasons for delays can be transport delays, delays in information transmission, delays in decision-making, etc. The most natural are delays when modeling objects in ecology, medicine, population dynamics, etc. Features of the dynamics of vehicles in different environments (water, land, air) can also be taken into account by introducing a delay. Other physical and technical interpretations are also possible, for example, the molecular distribution of thermal energy in various media (solid bodies, liquids, etc.) is modeled by heat conduction equations. The Green’s function of the first boundary value problem is constructed for the nonlinear equation of heat conduction with a deviation of the argument, its properties are investigated, and the formula for the solution is established.
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    The cauchy problem for quasilinear equation with nonstationary diffusion coefficient
    (2023) Drin, Yaroslav; Drin, Iryna; Drin, Svitlana
    The initial problem for the heat conduction equation with the inversion of the argument are considered and Green’s function are determined. The theorem declared that the Poisson’s formula determines the solution of the Cauchy problem considered and proved.
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    The first boundary value problem for the nonlinear equation of heat conduction with deviation of the argument
    (2022) Drin, Yaroslav; Drin, Iryna; Drin, Svitlana; Stetsko, Yuriy
    The initial-boundary problem for the heat conduction equation with the inversion of the argument are considered. The Green’s function of considered problem are determined. The theorem about the Poisson integral limitation is proved. The theorem declared that the Poisson integral determine the solution of the first boundary problem considered and proved.
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    Non-classical boundary value problem for the heat conduction equation
    (2024) Drin, Iryna; Drin, Svitlana; Drin, Yaroslav; Lutskiv, Mykhailo
    The first boundary value problem for the heat conduction equation was studied in. We provide the first proof of a formula for solving the non-classical boundary value problem, where the temperature is specified at the left end of a homogeneous rod and its flux at the right end.
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    Study of numerical and analytical solutions of a generalized boundary value problem for the heat conduction equation
    (2024) Drin, Iryna; Drin, Svitlana; Drin, Yaroslav; Lutskiv, Mykhailo
    The computed values of the solution obtained by the finite difference method and the results of the numerical investigation of the analytical solution of this problem match with maximum and average relative errors of +7.03% and ±1.82%, respectively. The graphs of the numerical and analytical solutions coincide over the entire range of investigated time and space values. Further improvements in the accuracy of the numerical solution can be achieved by adjusting grid parameters – reducing spatial step size and increasing the number of computational iterations.