Development of a method for solving elliptic differential equations based on a nonlinear compact-polynomial scheme

Kuzenov, Victor V.; Ryzhkov, Sergei V.; Varaksin, Aleksey Yu

doi:10.1016/j.cam.2024.116098

Journal of Computational and Applied Mathematics

2024

DOI: 10.1016/j.cam.2024.116098

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Development of a method for solving elliptic differential equations based on a nonlinear compact-polynomial scheme

Victor V. Kuzenov,

Sergei V. Ryzhkov,

Aleksey Yu Varaksin

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2024

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Cited by 4 publications

References 39 publications

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Radiation–Magnetogasdynamic Calculations in the Interaction of Powerful Energy Flows with Matter in a Magnetic Field

Kuzenov,

Ryzhkov

2024

Tech. Phys.

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Radiation–Magnetogasdynamic Calculations in the Interaction of Powerful Energy Flows with Matter in a Magnetic Field

Kuzenov,

Ryzhkov

2024

Tech. Phys.

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Physical Modeling of Structure and Dynamics of Concentrated, Tornado-like Vortices (A Review)

Varaksin,

Ryzhkov

2024

Aerospace

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Physical modeling is essential for developing the theory of concentrated, tornado-like vortices. Physical modeling data are crucial for interpreting real tornado field measurements and mathematical modeling data. This review focuses on describing and analyzing the results of a physical modeling of the structure and dynamics of tornado-like vortices, which are laboratory analogs of the vortex structures observed in nature (such as “dust devils” and air tornadoes). This review discusses studies on various types of concentrated vortices in laboratory conditions: (i) wall-bounded, stationary, and tornado-like vortices, (ii) wall-free, quasi-stationary, and tornado-like vortices, and (iii) wall-free, non-stationary, and tornado-like vortices. In our opinion, further progress in the development of the theory of non-stationary concentrated tornado-like vortices will determine the possibility of setting up the following studies: conducting experiments in order to study the mechanisms of vortex generation near the surface, determining the factors contributing to the stabilization (strengthening) and destabilization (weakening) of the generated vortices, and to find methods and means of controlling vortices.

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Lyapunov Inequalities for Systems of Tempered Fractional Differential Equations with Multi-Point Coupled Boundary Conditions via a Fix Point Approach

Ma,

2024

Fractal Fract

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In this paper, we study a system of nonlinear tempered fractional differential equations with multi-point coupled boundary conditions. By applying the properties of Green’s function and the operator and combining the method of matrix analysis, we obtain the corresponding Lyapunov inequalities under two Banach spaces. And, we have compared two Lyapunov inequalities under certain conditions. An example is given to verify our results.

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Development of a method for solving elliptic differential equations based on a nonlinear compact-polynomial scheme

Cited by 4 publications

References 39 publications

Radiation–Magnetogasdynamic Calculations in the Interaction of Powerful Energy Flows with Matter in a Magnetic Field

Radiation–Magnetogasdynamic Calculations in the Interaction of Powerful Energy Flows with Matter in a Magnetic Field

Physical Modeling of Structure and Dynamics of Concentrated, Tornado-like Vortices (A Review)

Lyapunov Inequalities for Systems of Tempered Fractional Differential Equations with Multi-Point Coupled Boundary Conditions via a Fix Point Approach

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