The differential-symbol method of solving the problem two-point in time for a nonhomogeneous partial differential equation

Nytrebych, Zinovii; Маланчук, Оксана

doi:10.1007/s10958-017-3574-2

Cited by 12 publications

(3 citation statements)

References 9 publications

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“…K C using a method from the opposite is reduced to proving the trivialness in this class of solution to problem (8), (7). The latter property follows from results of paper [46]. Comment 1.…”

Section: K Cmentioning

confidence: 69%

“…are also pairwise different and belong to the set M, Set M is to be selected so that class ,M K C is the class of unique solvability of problem (10),(7).Similarly to papers[45,46], we consider an entire function of vector-parameter well as the fact that function (12) is a quasipolynomial with respect to τ for any . s ν ∈C Let L be the set of zeros of function(12), then put \ , in equation(10), which predetermines a wave process, is to be considered a quasi-polynomial, which belongs to , ,…”

mentioning

confidence: 99%

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Analytical method to study a mathematical model of wave processes under twopoint time conditions

Nytrebych

Ільків

Пукач

et al. 2019

EEJET

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Adequate mathematical modeling of wave processes in oscillatory systems plays an important role in modern approaches to solving a series of scientific and engineering tasks, which arise in the problems on analysis, synthesis, and optimization of parameters for machine-building structures. Mathematical and numerical modelling are important in understanding the essence of phenomena and processes that are studied in modern mechanics and physics. Considering the adequacy of mathematical models and methods of analysis contributes to the interpretation of existing, as well as prediction and discovery of new, phenomena. Modern industrial equipment is operated in a wide range of parameters, particularly at high speeds, high pressures and energies, etc. The specified reasons necessitate the study and analysis

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Section: K Cmentioning

confidence: 69%

mentioning

confidence: 99%

Analytical method to study a mathematical model of wave processes under twopoint time conditions

Nytrebych

Ільків

Пукач

et al. 2019

EEJET

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“…Consider a two-point problem with two-point conditions in the form of a constant voltage applied along a line at the initial moment of time = 0 and at some other point in time = . Using the differential-symbol method [17][18][19][20], we can write a generalized solution of the two-point problem (3), (4) in the following form:…”

Section: A Two-point Problem With a Constant Voltage Along A Long Linementioning

confidence: 99%

Simulation of the Propagation of Electromagnetic Oscillations by the Method of the Modified Equation of the Telegraph Line

Politansky

Nytrebych

Petryshyn

et al. 2021

Phys. Chem. Solid St.

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The article considers the physical processes associated with the propagation of electromagnetic oscillations in a long line, the size of which is the same or slightly greater than the length of the electromagnetic wave (not more than ten times). As a research method, the differential-symbolic method is used, which is applied to the modified equation of the telegraph line. The boundary conditions for the two-point problem as well as additional parameters that are coefficients for the first derivatives in terms of coordinate and time in comparison with the classical equation of the telegraph line are considered as parameters for controlling the process of propagation of electromagnetic oscillations. Based on the differential-symbolic method, the boundary conditions of the two-point problem are found, under which the most characteristic oscillatory processes are realized in a long line. Based on the research, it is possible to draw conclusions about the effectiveness of analytical methods for the analysis of specific technical objects and control of the processes that take place in them.

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The Two-Point Problem as the Mathematical Model of the Oscillation Process of a Longitudinal Body

Nytrebych

Маланчук

2020

Advances in Intelligent Systems and Computing

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The differential-symbol method of solving the problem two-point in time for a nonhomogeneous partial differential equation

Cited by 12 publications

References 9 publications

Analytical method to study a mathematical model of wave processes under twopoint time conditions

Analytical method to study a mathematical model of wave processes under twopoint time conditions

Simulation of the Propagation of Electromagnetic Oscillations by the Method of the Modified Equation of the Telegraph Line

The Two-Point Problem as the Mathematical Model of the Oscillation Process of a Longitudinal Body

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The differential-symbol method of solving the problem two-point in time for a nonhomogeneous partial differential equation

Cited by 12 publications

References 9 publications

Analytical method to study a mathematical model of wave processes under two­point time conditions

Analytical method to study a mathematical model of wave processes under two­point time conditions

Simulation of the Propagation of Electromagnetic Oscillations by the Method of the Modified Equation of the Telegraph Line

The Two-Point Problem as the Mathematical Model of the Oscillation Process of a Longitudinal Body

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Analytical method to study a mathematical model of wave processes under twopoint time conditions

Analytical method to study a mathematical model of wave processes under twopoint time conditions