scholarly journals Study of dynamics of bilinear systems with parameter

2021 ◽  
Vol 80 (2) ◽  
pp. 47-54
Author(s):  
L. Kh. Zhunussova ◽  
Keyword(s):  
Numerical Calculation ◽  
Differential Equations ◽  
Bilinear System ◽  
Bilinear Systems ◽  
System Of Differential Equations ◽  
Systems Of Differential Equations ◽  
Computational Processes

A number of problems in biology, ecology and chemistry can be reduced to the consideration of n-dimensional nonlinear, in particular, bilinear systems of differential equations containing a parameter. For such systems, it is of interest to find a solution to the influence of a parameter. Complex computational processes arising in the modeling of the above systems make it possible for research on this topic to remain always relevant. In this paper, a bilinear system of differential equations is considered. The numerical calculation of the solution of this system is presented.

scholarly journals Framework for generalized polytropes with complexity factor

2019 ◽  
Vol 79 (12) ◽  
Author(s):  
Shiraz Khan ◽  
S. A. Mardan ◽  
M. A. Rehman
Keyword(s):  
Equation Of State ◽  
Energy Density ◽  
Differential Equations ◽  
Spherical Symmetry ◽  
Mass Density ◽  
Fluid Distribution ◽  
System Of Differential Equations ◽  
Systems Of Differential Equations ◽  
Polytropic Equation

AbstractA framework is developed for generalized polytropes with the help of complexity factor introduced by Herrera (Phy Rev D 97:044010, 2018), by using the spherical symmetry with anisotropic inner fluid distribution. For this purpose generalized polytropic equation of state will be used, having two cases (i) for mass density $$(\mu _{o})$$(μo), (ii) for energy density $$(\mu )$$(μ), each case leads to a system of differential equations. These systems of differential equations involve two equations with three unknowns and they will be made consistent by using the complexity factor. The analysis of the solutions of these systems will be carried out graphically by using different parametric values involved in the systems.

scholarly journals Bilateral approximations and periodic solutions of systems of differential equations with impulses

1985 ◽  
Vol 31 (2) ◽  
pp. 293-307
Author(s):  
S.G. Hristova ◽  
D.D. Bainov
Keyword(s):  
Periodic Solution ◽  
Linear System ◽  
Differential Equations ◽  
Periodic Solutions ◽  
System Of Differential Equations ◽  
Systems Of Differential Equations ◽  
Non Linear ◽  
Impulsive Perturbations ◽  
Non Linear System

The paper justifies a method of bilateral approximations for finding the periodic solution of a non-linear system of differential equations with impulsive perturbations at fixed moments of time.

The Solution of Non-Homogeneous Systems of Differential Equations by Undetermined Coefficients

1966 ◽  
Vol 9 (4) ◽  
pp. 481-487
Author(s):  
Fred Brauer
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Linear Algebra ◽  
Single Equation ◽  
Analogous Problem ◽  
System Of Differential Equations ◽  
Homogeneous Differential Equation ◽  
Homogeneous Systems ◽  
Systems Of Differential Equations ◽  
Straightforward Extension

The solution of a linear non-homogeneous differential equation whose non-homogeneous term is of the form tkeαt can be obtained by what is usually called the method of undetermined coefficients. The application of this method may be justified in several different ways (see for example [1, pp. 114–117], [2, pp. 94–99], [3]).We shall consider the analogous problem for a system of differential equations. It turns out that we can solve this problem using only elementary techniques of linear algebra. The solution has essentially the same form as in the case of a single equation, but may contain terms which would not be expected and may lack terms which would be expected in a straightforward extension of the theory to systems. Our method of obtaining the solution is constructive, in the sense that while our results give only the form of the solution, the solution itself may be found by substitution of this form into the system of differential equations.

scholarly journals Two hybrid and non-hybrid k-dimensional inclusion systems via sequential fractional derivatives

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Seher Melike Aydogan ◽  
Fethiye Muge Sakar ◽  
Mostafa Fatehi ◽  
Shahram Rezapour ◽  
Hashem Parvaneh Masiha
Keyword(s):  
Differential Equations ◽  
Fractional Derivatives ◽  
Existence Of Solutions ◽  
Integral Boundary Conditions ◽  
System Of Differential Equations ◽  
Integral Boundary ◽  
Systems Of Differential Equations ◽  
Complex Phenomena ◽  
Two Hybrid ◽  
Better Than

AbstractSome complicated events can be modeled by systems of differential equations. On the other hand, inclusion systems can describe complex phenomena having some shocks better than the system of differential equations. Also, one of the interests of researchers in this field is an investigation of hybrid systems. In this paper, we study the existence of solutions for hybrid and non-hybrid k-dimensional sequential inclusion systems by considering some integral boundary conditions. In this way, we use different methods such as α-ψ contractions and the endpoint technique. Finally, we present two examples to illustrate our main results.

SOLUTION OF SOME SYSTEMS OF DIFFERENTIAL EQUATIONS IN MATHEMATICAL SYSTEM MAPLE

2013 ◽  
Vol 1 (05) ◽  
pp. 58-65
Author(s):  
Yunona Rinatovna Krakhmaleva ◽  
◽  
Gulzhan Kadyrkhanovna Dzhanabayeva ◽  
Keyword(s):  
Differential Equations ◽  
Systems Of Differential Equations ◽  
Mathematical System

On decomposability of countable systems of differential equations

1993 ◽  
Vol 45 (10) ◽  
pp. 1598-1608
Author(s):  
A. M. Samoilenko ◽  
Yu. V. Teplinskii
Keyword(s):  
Differential Equations ◽  
Systems Of Differential Equations

scholarly journals Outflowing Envelopes From Stars at Arbitrary Optical Depths a New Approach to the Problem

1998 ◽  
Vol 11 (1) ◽  
pp. 381-381
Author(s):  
A.V. Dorodnitsyn
Keyword(s):  
Differential Equations ◽  
Massive Star ◽  
System Of Differential Equations ◽  
Continuous Transition ◽  
Satisfactory Description ◽  
Sonic Point ◽  
New Approach ◽  
Star Evolution ◽  
Matter Flux ◽  
Massive Star Evolution

We have considered a stationary outflowing envelope accelerated by the radiative force in arbitrary optical depth case. Introduced approximations provide satisfactory description of the behavior of the matter flux with partially separated radiation at arbitrary optical depths. The obtained systemof differential equations provides a continuous transition of the solution between optically thin and optically thick regions. We analytically derivedapproximate representation of the solution at the vicinity of the sonic point. Using this representation we numerically integrate the system of equations from the critical point to the infinity. Matching the boundary conditions we obtain solutions describing the problem system of differential equations. The theoretical approach advanced in this work could be useful for self-consistent simulations of massive star evolution with mass loss.

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