scholarly journals An approximate solution of the one class third order onlinear differential equation in the analyticity domain

2020 ◽  
pp. 45-54
Author(s):  
Виктор Николаевич Орлов ◽  
Рио-Рита Вадимовна Разакова
Keyword(s):  
Approximate Solution ◽  
Existence And Uniqueness ◽  
A Priori Estimates ◽  
Nonlinear Differential Equations ◽  
A Priori ◽  
Existence And Uniqueness Theorem ◽  
Third Order ◽  
Analyticity Domain ◽  
Priori Estimates ◽  
The One

В работе рассмотрен класс нелинейных дифференциальных уравнений третьего порядка с полиномиальной правой частью шестой степени. Доказана теорема существования и единственности решения в области аналитичности. Построено аналитическое приближенное решение. Предложен вариант оптимизации априорных оценок с помощью апостериорных. Проведен численный эксперимент. There is a class of third-order nonlinear differential equations with polynomial right part of the sixth degree considered in the paper. The existence and uniqueness theorem of a solution in the domain of analyticity is proved by authors. There is an analytical approximate solution which was constructed by V. Orlov and R. Razakova. A variant of optimization of a priori estimates using posterior ones is proposed by authors. A numerical experiment is carried out too.

scholarly journals Existence theorem for a solution of a class of third order nonlinear differential equations with polynomial right hand side of the seventh degree in a vicinity of a movable singular point

2020 ◽  
pp. 92-100
Author(s):  
Виктор Николаевич Орлов ◽  
Магомедюсуф Владимирович Гасанов
Keyword(s):  
Differential Equations ◽  
A Priori Estimates ◽  
Nonlinear Differential Equations ◽  
A Priori ◽  
A Posteriori ◽  
Existence And Uniqueness Theorem ◽  
Third Order ◽  
Priori Estimates ◽  
A Priori Estimation ◽  
Posteriori Estimation

В настоящей статье дано развитие варианта доказательства теоремы существования и единственности решения рассматриваемого класса нелинейных дифференциальных уравнений, характерной особенностью которых является наличие подвижных особых точек. Представленное доказательство позволяет построить аналитическое приближенное решение, получить его априорные оценки. Апостериорная оценка позволяет оптимизировать априорную оценку. Теоретический материал протестирован с помощью численного эксперимента. This article gives the development of a version of the proof of the existence and uniqueness theorem for the solution of the class of nonlinear differential equations under consideration whose characteristic feature is the presence of movable singular points. The presented proof allows us to construct an analytical approximate solution and obtain its a priori estimates. A posteriori estimation allows to optimize a priori estimation. The theoretical material is tested using a numerical experiment.

scholarly journals Research of a third-order nonlinear differential equation in the vicinity of a moving singular point for a complex plane

2021 ◽  
Vol 263 ◽  
pp. 03019
Author(s):  
Victor Orlov ◽  
Magomedyusuf Gasanov
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Nonlinear Differential Equation ◽  
A Priori Estimates ◽  
A Priori ◽  
Third Order ◽  
Modified Method ◽  
Order Nonlinear Differential Equation ◽  
Priori Estimates ◽  
The Right

This article generalizes the previously obtained results of existence and uniqueness theorems for the solution of a third-order nonlinear differential equation in the vicinity of moving singular points in the complex domain, as well as constructs an analytical approximate solution, and obtains a priori estimates of the error of this approximate solution. The study was carried out using the modified method of majorants to solve this equation, which differs from the classical theory, in which this method is applied to the right-hand side of the equation The final point of the article is to conduct a numerical experiment to test the theoretical positions obtained.

scholarly journals Analytical solution of a class of nonlinear differential equations of the third order in the complex area

2021 ◽  
pp. 75-84
Author(s):  
Виктор Николаевич Орлов ◽  
Людмила Витальевна Мустафина
Keyword(s):  
Analytical Solution ◽  
Differential Equations ◽  
A Priori Estimates ◽  
Nonlinear Differential Equations ◽  
A Priori ◽  
A Priori Estimate ◽  
Third Order ◽  
The Third ◽  
Change Of Variables ◽  
Priori Estimates

В работе приводится доказательство теоремы существования и единственности аналитического решения класса нелинейных дифференциальных уравнений третьего порядка, правая часть которого представлена полиномом шестой степени, в комплексной области. Расширен класс рассматриваемых уравнений за счет новой замены переменных. Получена априорная оценка аналитического приближенного решения. Представлен вариант численного эксперимента оптимизации априорных оценок с помощью апостериорных. The article presents a proof of the theorem of the existence and uniqueness of the analytical solution of the class of nonlinear differential equations of the third order, with a polynomial right-hand side of the sixth degree, in the complex domain. The class of the considered equations has been extended by means of a new change of variables. An a priori estimate of the analytical approximate solution is obtained. A variant of the numerical experiment of optimizing a priori estimates using a posteriori estimates is presented.

scholarly journals The Cauchy–Neumann and Cauchy–Robin problems for a class of hyperbolic operators with double characteristics in presence of transition

2020 ◽  
Vol 11 (4) ◽  
pp. 1991-2022
Author(s):  
Annamaria Barbagallo ◽  
Vincenzo Esposito
Keyword(s):  
Sobolev Spaces ◽  
Existence And Uniqueness ◽  
A Priori Estimates ◽  
A Priori ◽  
Existence And Uniqueness Results ◽  
Mixed Problems ◽  
Uniqueness Results ◽  
Hyperbolic Operators ◽  
Priori Estimates

Abstract The mixed Cauchy–Neumann and Cauchy–Robin problems for a class of hyperbolic operators with double characteristics in presence of transition is investigated. Some a priori estimates in Sobolev spaces with negative indexes are proved. Subsequently, existence and uniqueness results for the mixed problems are obtained.

A difference scheme for equations of ocean dynamics on unstructured grids

2014 ◽  
Vol 29 (3) ◽  
Author(s):  
Alexey V. Drutsa
Keyword(s):  
Difference Scheme ◽  
Existence And Uniqueness ◽  
Large Scale ◽  
A Priori Estimates ◽  
Unstructured Grids ◽  
A Priori ◽  
Ocean Dynamics ◽  
Priori Estimates ◽  
Uniqueness Of The Solution ◽  
Grid Operators

AbstractA difference scheme on unstructured grids is constructed for the system of equations of large scale ocean dynamics. The properties of the grid problem and grid operators are studied, in particular, a series of a priori estimates and the theorem on existence and uniqueness of the solution are proved.

On Approximations to Solutions of Nonlinear Integral Equations of the Urysohn Type

1973 ◽  
Vol 16 (1) ◽  
pp. 137-141
Author(s):  
K. A. Zischka
Keyword(s):  
Existence And Uniqueness ◽  
A Priori Estimates ◽  
A Priori ◽  
Sufficient Conditions ◽  
Successive Approximations ◽  
Uniqueness Of Solutions ◽  
Nonlinear Integral Equations ◽  
Priori Estimates ◽  
The Given ◽  
Uniqueness Of A Solution

This note will derive a priori estimates of the errors due to replacing the given integral operator A by a similar operator A* of the same type when successive approximations are applied to the integral equation φ=Aφ.The existence and uniqueness of solutions to this equation follow easily by applying a well known fixed point theorem in a Banach space to the above mapping [1, 2]. Moreover, sufficient conditions for the existence and uniqueness of a solution to Urysohn's equation are stated explicitly in a note by the author [3].

ASYMPTOTIC BEHAVIOR OF STOCHASTIC DISSIPATIVE QUANTUM ZAKHAROV EQUATIONS

2013 ◽  
Vol 13 (02) ◽  
pp. 1250016 ◽  
Author(s):  
YANFENG GUO ◽  
BOLING GUO ◽  
DONGLONG LI
Keyword(s):  
Asymptotic Behavior ◽  
White Noise ◽  
Approximation Method ◽  
Existence And Uniqueness ◽  
A Priori Estimates ◽  
A Priori ◽  
Galerkin Approximation ◽  
Uniqueness Of Solutions ◽  
Asymptotic Behaviors ◽  
Priori Estimates

The stochastic dissipative quantum Zakharov equations with white noise are studied. The existence and uniqueness of solutions are obtained by using the standard Galerkin approximation method on the basis of the time uniform a priori estimates in various spaces. Moreover, the asymptotic behaviors of the solutions for the stochastic dissipative quantum Zakharov equations with white noise are also investigated.

Numerical analysis of nonlinear model of excited carrier decay

2013 ◽  
Vol 11 (6) ◽  
Author(s):  
Natalija Tumanova ◽  
Raimondas Čiegis ◽  
Mečislavas Meilūnas
Keyword(s):  
Differential Equations ◽  
A Priori Estimates ◽  
Nonlinear Differential Equations ◽  
A Priori ◽  
Euler Method ◽  
Genetic Optimization ◽  
Identifiability Analysis ◽  
Priori Estimates ◽  
Backward Euler ◽  
Excited Carrier

AbstractThis paper presents a mathematical model for photo-excited carrier decay in a semiconductor. Due to the carrier trapping states and recombination centers in the bandgap, the carrier decay process is defined by the system of nonlinear differential equations. The system of nonlinear ordinary differential equations is approximated by linearized backward Euler scheme. Some a priori estimates of the discrete solution are obtained and the convergence of the linearized backward Euler method is proved. The identifiability analysis of the parameters of deep centers is performed and the fitting of the model to experimental data is done by using the genetic optimization algorithm. Results of numerical experiments are presented.

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