scholarly journals The comparative analysis of approximating methods of the solution of the nonlinear differential equations

2010 ◽  
Vol 1 (23) ◽  
Author(s):  
Е.В. Киркач
Keyword(s):  
Comparative Analysis ◽  
Differential Equations ◽  
Nonlinear Differential Equations

scholarly journals BEHAVIOR OF THE PHARMACOKINETICS OF ENROFLOXACIN IN THE PHASE SPACE

2019 ◽  
Vol 7 (4) ◽  
pp. 288-293
Author(s):  
Miroslav Vasilev ◽  
Galya Shivacheva
Keyword(s):  
Comparative Analysis ◽  
Plasma Concentration ◽  
Phase Space ◽  
Differential Equations ◽  
Mathematical Models ◽  
Blood Plasma ◽  
Graphical Representation ◽  
Nonlinear Differential Equations ◽  
Qualitative Assessment ◽  
Second Order Differential Equations

Phase space is an approach for analysis of nonlinear differential equations. The graphical solutions that are obtained are convenient for qualitative assessment of the behavior of systems and processes. A comparative analysis of the pharmacokinetics of the antibiotic enrofloxacin administered intravenously in dogs and cats has been performed in the present study. The mathematical models that represent the change in blood plasma concentration of the two groups of animals are described by second-order differential equations. For the graphical representation of phase trajectories using the fluoroquinolone, the Mathcad program tools are used. The properties of the peculiar points are determined based on the received images.

scholarly journals ANALYSIS OF FORCED VIBRATIONS OF NONLINEAR PLATES IN A VISCOELASTIC MEDIUM UNDER THE CONDITIONS OF THE DIFFERENT COMBINATIONAL INTERNAL

2019 ◽  
Vol 15 (3) ◽  
pp. 131-148
Author(s):  
Marina Shitikova ◽  
Vladimir Kandu
Keyword(s):  
Comparative Analysis ◽  
Differential Equations ◽  
Dynamic Response ◽  
Fractional Derivative ◽  
Viscoelastic Medium ◽  
Nonlinear Differential Equations ◽  
Forced Vibrations ◽  
Numerical Calculations ◽  
Free And Forced Vibrations ◽  
Nonlinear Plate

In the present paper, the force driven dynamic response of a nonlinear plate embedded in a viscoelastic medium, damping features of which are described by the Kelvin-Voigt fractional derivative model, is studied. The motion of the plate is described by three coupled nonlinear differential equations with due account for the fact that the plate is being under the conditions of the internal combinational resonance accompanied by the external resonance, resulting in the interaction of three modes corresponding to the mutually orthogonal displacements. A comparative analysis of numerical calculations for the cases of free and forced vibrations has been carried out.

BEHAVIOR OF THE PHARMACOKINETICS OF ENROFLOXACIN IN THE PHASE SPACE

2019 ◽  
pp. 77-83
Author(s):  
Miroslav Vasilev ◽  
Galya Shivacheva
Keyword(s):  
Comparative Analysis ◽  
Plasma Concentration ◽  
Phase Space ◽  
Differential Equations ◽  
Mathematical Models ◽  
Blood Plasma ◽  
Graphical Representation ◽  
Nonlinear Differential Equations ◽  
Qualitative Assessment ◽  
Second Order Differential Equations

Phase space is an approach for analysis of nonlinear differential equations. The graphical solutions that are obtained are convenient for qualitative assessment of the behavior of systems and processes. A comparative analysis of the pharmacokinetics of the antibiotic enrofloxacin administered intravenously in dogs and cats has been performed in the present study. The mathematical models that represent the change in blood plasma concentration of the two groups of animals are described by second-order differential equations. For the graphical representation of phase trajectories using the fluoroquinolone, the Mathcad program tools are used. The properties of the peculiar points are determined based on the received images.

Application of the exp(-φ)-expansion method to the Pochhammer-Chree equation

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3347-3354 ◽  
Author(s):  
Nematollah Kadkhoda ◽  
Michal Feckan ◽  
Yasser Khalili
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Present Article ◽  
Analytical Solutions ◽  
Nonlinear Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Rational Functions ◽  
Expansion Method ◽  
Exponential Functions

In the present article, a direct approach, namely exp(-?)-expansion method, is used for obtaining analytical solutions of the Pochhammer-Chree equations which have a many of models. These solutions are expressed in exponential functions expressed by hyperbolic, trigonometric and rational functions with some parameters. Recently, many methods were attempted to find exact solutions of nonlinear partial differential equations, but it seems that the exp(-?)-expansion method appears to be efficient for finding exact solutions of many nonlinear differential equations.

scholarly journals Solving nonlinear differential equations with differentiable quantum circuits

2021 ◽  
Vol 103 (5) ◽  
Author(s):  
Oleksandr Kyriienko ◽  
Annie E. Paine ◽  
Vincent E. Elfving
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Quantum Circuits

scholarly journals Nonlinear Differential Equations Modeling the Antarctic Circumpolar Current

2021 ◽  
Vol 23 (4) ◽  
Author(s):  
Jifeng Chu ◽  
Kateryna Marynets
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Topological Degree ◽  
Antarctic Circumpolar Current ◽  
Fixed Point Theorems ◽  
Nonlinear Differential Equations ◽  
Existence Results ◽  
Circumpolar Current ◽  
The Antarctic

AbstractThe aim of this paper is to study one class of nonlinear differential equations, which model the Antarctic circumpolar current. We prove the existence results for such equations related to the geophysical relevant boundary conditions. First, based on the weighted eigenvalues and the theory of topological degree, we study the semilinear case. Secondly, the existence results for the sublinear and superlinear cases are proved by fixed point theorems.

Asymptotics for third-order nonlinear differential equations: Non-oscillatory and oscillatory cases

2021 ◽  
pp. 1-19
Author(s):  
Calogero Vetro ◽  
Dariusz Wardowski
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Nonlinear Differential Equations ◽  
Oscillatory Behavior ◽  
Third Order ◽  
First Order ◽  
Third Order Differential Equation ◽  
Comparison Technique ◽  
First Order Differential Equations

We discuss a third-order differential equation, involving a general form of nonlinearity. We obtain results describing how suitable coefficient functions determine the asymptotic and (non-)oscillatory behavior of solutions. We use comparison technique with first-order differential equations together with the Kusano–Naito’s and Philos’ approaches.

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