Existence and Uniqueness Theorem for a Solution to a Class of a Third-Order Nonlinear Differential Equation in the Domain of Analyticity

Orlov, V. N.; Gasanov, Magomedyusuf

doi:10.3390/axioms11050203

Cited by 3 publications

(3 citation statements)

References 12 publications

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“…Equation ( 9) is nonlinear with respect to ω(t). If A depends on t, then the author's analytical approximate solution method is needed [26][27][28][29][30][31]. In the case when A does not depend on t, we can consider t(ω) which is the inverse function for ω(t) and, taking into account the initial conditions ω(0) = 1, t(1) = 0, it is possible to solve the Equation ( 9) in quadratures.…”

Section: An Estimate Of the Ratio Of Static And Total Pressure Centri...mentioning

confidence: 99%

Mathematical Calculation of Synchronous Electric Motors Dynamic Stability

Pupin,

Orlov

2023

Mathematics

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This paper considers the equipment and power supply schemes for urban water supply, heat supply and sewerage pumping stations. Mathematical calculations of the impact of the static and full centrifugal pumps pressure ratio on the dynamic stability of synchronous electric motors were carried out. An analysis of the influence of pump parameters and engine load on the run-down parameters and drive stability during power shutdowns was carried out. It has been theoretically proven and practically confirmed that ensuring the stability of pumping station drives and the reduction in enterprise losses during various short-term disruptions in power supply networks can be provided by means of a high-speed backup source with a response time of less than 9 ms, dynamic voltage dip compensators with a response time of less than 3 ms and uninterruptible power supply sources.

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Section: An Estimate Of the Ratio Of Static And Total Pressure Centri...mentioning

confidence: 99%

Mathematical Calculation of Synchronous Electric Motors Dynamic Stability

Pupin,

Orlov

2023

Mathematics

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“…These ideas were developed for other nonlinear differential equations in [23,25]. In particular, the existence of movable singular points in the Van der Pole equation has been proven in [23].…”

Section: Introductionmentioning

confidence: 99%

“…In particular, the existence of movable singular points in the Van der Pole equation has been proven in [23]. A generalization of the modified majorant method for third-order nonlinear differential equation in the domain of analyticity was represented in [25]. An analytical approximate solution was built, taking into account the solution search domain.…”

Section: Introductionmentioning

confidence: 99%

The Influence of the Perturbation of the Initial Data on the Analytic Approximate Solution of the Van der Pol Equation in the Complex Domain

Orlov

Chichurin

2023

Symmetry

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In this paper, we substantiate the analytical approximate method for Cauchy problem of the Van der Pol equation in the complex domain. These approximate solutions allow analytical continuation for both real and complex cases. We follow the influence of variation in the initial data of the problem in order to control the computational process and improve the accuracy of the final results. Several simple applications of the method are given. A numerical study confirms the consistency of the developed method.

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A Nonlinear System of Differential Equations in Supercritical Flow Spread Problem and Its Solution Technique

Evtushenko

2022

Axioms

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A nonlinear system of differential equations in the problem of free flowing of supercritical flow is considered and a method of its solution is proposed. The analytical method is based on the introduction of the velocity hodograph plane and the obtaining of analytical solutions for the system of partial differential equations. It is pointed out that apart from being purely analytical, the potential flow model has a great practical demand due to its use as a base for the further research of the flow resistance forces. The proposed model can be developed by taking into account flow resistance and gradient, the bottom of the diverting channel flow. The theoretical results are complemented by numerical experiments and compared with experimental data.

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Existence and Uniqueness Theorem for a Solution to a Class of a Third-Order Nonlinear Differential Equation in the Domain of Analyticity

Cited by 3 publications

References 12 publications

Mathematical Calculation of Synchronous Electric Motors Dynamic Stability

Mathematical Calculation of Synchronous Electric Motors Dynamic Stability

The Influence of the Perturbation of the Initial Data on the Analytic Approximate Solution of the Van der Pol Equation in the Complex Domain

A Nonlinear System of Differential Equations in Supercritical Flow Spread Problem and Its Solution Technique

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