Log in

Relevant bibliographies by topics / Differential equations system / Journal articles

To see the other types of publications on this topic, follow the link: Differential equations system.

Journal articles on the topic 'Differential equations system'

Author: Grafiati

Published: 5 June 2025

Last updated: 24 June 2025

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Differential equations system.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

Esanov, Nuriddin Kurbanovich. "RESOLVING SYSTEM OF DIFFERENTIAL EQUATIONS." Modern Scientific Research International Scientific Journal 2, no. 1 (2024): 241–45. https://doi.org/10.5281/zenodo.10640698.

Full text

Abstract:

This paper mainly used moment equations along the longitudinal, transverse and <em>x</em>, <em>y</em> axes. In this system of six differential equilibrium equations, the force coefficients are calculated as seven. Taking into account the system of equations (1), the system of linear equations was reduced to five equations. After finding the components of deformation from the system of equations (5) - (8), the forces in the state of deformation are found using elasticity relations (1). If we accept , then (5)-(7) are translated into a system of four equations for an open profile rod.

APA, Harvard, Vancouver, ISO, and other styles

2

Alcorta-García, María Aracelia, Martín Eduardo Frías-Armenta, María Esther Grimaldo-Reyna, and Elifalet López-González. "Algebrization of Nonautonomous Differential Equations." Journal of Applied Mathematics 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/632150.

Full text

Abstract:

Given a planar system of nonautonomous ordinary differential equations,dw/dt=F(t,w), conditions are given for the existence of an associative commutative unital algebraAwith uniteand a functionH:Ω⊂R2×R2→R2on an open setΩsuch thatF(t,w)=H(te,w)and the mapsH1(τ)=H(τ,ξ)andH2(ξ)=H(τ,ξ)are Lorch differentiable with respect toAfor all(τ,ξ)∈Ω, whereτandξrepresent variables inA. Under these conditions the solutionsξ(τ)of the differential equationdξ/dτ=H(τ,ξ)overAdefine solutions(x(t),y(t))=ξ(te)of the planar system.

APA, Harvard, Vancouver, ISO, and other styles

3

Petryna, G., and A. Stanzhytskyi. "APPROXIMATION OF STOCHASTIC DELAY DIFFERENTIAL SYSTEMS BY A STOCHASTIC SYSTEM WITHOUT DELAY." Bukovinian Mathematical Journal 12, no. 1 (2024): 120–36. http://dx.doi.org/10.31861/bmj2024.01.11.

Full text

Abstract:

In this paper, we propose a scheme for approximating the solutions of stochastic differential equations with delay by solutions of stochastic differential equations without delay. Stochastic delay differential equations play a crucial role in modeling real-world processes where the evolution depends on past states, introducing complexities due to their infinite-dimensional phase space. To overcome these difficulties, we develop an approach based on approximating the delay system by an ordinary differential equation system of increased dimension. Our main result is to prove that, under certain conditions, the solutions of the approximating system converge in the mean square sense to the solutions of the original delay system. This approach allows for effective analysis and modeling of stochastic systems with delay using finite-dimensional stochastic differential equations without delay.

APA, Harvard, Vancouver, ISO, and other styles

4

BILYI, Leonid, Oleh POLISHCHUK, Svitlana LISEVICH, Anatoly ZALIZETSKY, and Vasiliy MELNIK. "MODELING OF NONLINEAR DYNAMIC SYSTEMS ON THE BASIS OF THE SYSTEM SENSITIVITY MODEL TO ITS INITIAL CONDITIONS." Herald of Khmelnytskyi National University. Technical sciences 309, no. 3 (2022): 99–103. http://dx.doi.org/10.31891/2307-5732-2022-309-3-99-103.

Full text

Abstract:

A typical approach for building and analyzing an object model is presented. It is determined that the tasks of analysis of nonlinear systems consist of: calculation of transients and established processes; determination of static and dynamic stability of the found processes; calculation of the sensitivity of the initial characteristics of the system to changes in its internal and external parameters. It is established that the efficiency of the analysis as a whole is determined not only by the efficiency of the algorithms of each of the stages of calculation, but also by the consistency of the mathematical apparatus that underlies them. It is determined that the calculation of transients is reduced to a problem with initial conditions in which the values of dependent variables are set for the same value of the independent variable, namely time. It is determined that nonlinear dynamic systems whose models are built on the qualitative theory of general differential equations are the main tool for solving many practical problems. It is established that this is explained by the following factors: the presence of a well-developed analytical apparatus and numerous methods of solving general differential equations; transparency and naturalness of general differential equations as a mathematical model to describe the process of transition of real objects from one state to another for external and internal causes; The availability of public qualitative methods of studying decisions of general differential equations, in particular methods of evaluation of stability, analysis of behavior within special points and their asymptotic behavior. The circumstances that lead to the fact that the systems described by conventional differential equations are a methodically very convenient material to create general algorithms for the study of dynamic systems. A mathematical model of sensitivity to the initial conditions is constructed on the basis of heterogeneous differential equations of the first variation, which opens up opportunities for solving the basic problems of analysis, which are: calculation of transitional processes and processes that have been established; Determination of static stability and calculation of parametric sensitivity, on the basis of a single algorithm for solving a two-point T-periodic marginal problem for conventional nonlinear differential equations.

APA, Harvard, Vancouver, ISO, and other styles

5

Cai, Xin. "Numerical Simulation for the System of Ordinary Differential Equations." Advanced Materials Research 179-180 (January 2011): 37–42. http://dx.doi.org/10.4028/www.scientific.net/amr.179-180.37.

Full text

Abstract:

Two coupled small parameter ordinary differential equations were considered. The solutions of differential equations will change rapidly near both sides of the boundary layer. Firstly, the properties were studied for differential equations. Secondly, the asymptotic properties of differential equations were discussed. Thirdly, the numerical methods with zero approximation were constructed for both left side and right side singular component differential equations. Finally, error analyses were given.

APA, Harvard, Vancouver, ISO, and other styles

6

Zhuk, Anastasia I., and Helena N. Zashchuk. "On associated solutions of the system of non-autonomous differential equations in the Lebesgue spaces." Journal of the Belarusian State University. Mathematics and Informatics, no. 1 (April 14, 2022): 6–13. http://dx.doi.org/10.33581/2520-6508-2022-1-6-13.

Full text

Abstract:

Herein, we investigate systems of non-autonomous differential equations with generalised coefficients using the algebra of new generalised functions. We consider a system of non-autonomous differential equations with generalised coefficients as a system of equations in differentials in the algebra of new generalised functions. The solution of such a system is a new generalised function. It is shown that the different interpretations of the solutions of the given systems can be described by a unique approach of the algebra of new generalised functions. In this paper, for the first time in the literature, we describe associated solutions of the system of non-autonomous differential equations with generalised coefficients in the Lebesgue spaces Lp(T).

APA, Harvard, Vancouver, ISO, and other styles

7

Sujito, S., L. Liliasari, and A. Suhandi. "Differential equations: Solving the oscillation system." Journal of Physics: Conference Series 1869, no. 1 (2021): 012163. http://dx.doi.org/10.1088/1742-6596/1869/1/012163.

Full text

APA, Harvard, Vancouver, ISO, and other styles

8

Brennan, Micheal, and Finbarr Holland. "Linear System of Impulsive Differential Equations." Irish Mathematical Society Bulletin 0038 (1997): 9–20. http://dx.doi.org/10.33232/bims.0038.9.20.

Full text

APA, Harvard, Vancouver, ISO, and other styles

9

Abirov, A. K., N. K. Shazhdekeeva, and T. N. Akhmurzina. "DIFFERENTIAL EQUATIONS IN A HYPERCOMPLEX SYSTEM." BULLETIN Series of Physics & Mathematical Sciences 69, no. 1 (2020): 7–11. http://dx.doi.org/10.51889/2020-1.1728-7901.01.

Full text

Abstract:

The article considers the problem of solving an inhomogeneous first-order differential equation with a variable with a constant coefficient in a hypercomplex system. The structure of the solution in different cases of the right-hand side of the differential equation is determined. The structure of solving the equation in the case of the appearance of zero divisors is shown. It turns out that when the component of a hypercomplex function is a polynomial of an independent variable, the differential equation turns into an inhomogeneous system of real variables from n equations and its solution is determined by certain methods of the theory of differential equations. Thus, obtaining analytically homogeneous solutions of inhomogeneous differential equations in a hypercomplex system leads to an increase in the efficiency of modeling processes in various fields of science and technology.

APA, Harvard, Vancouver, ISO, and other styles

10

Shan, Li Jun, Xue Fang, and Wei Dong He. "Nonlinear Dynamic Model and Equations of RV Transmission System." Advanced Materials Research 510 (April 2012): 536–40. http://dx.doi.org/10.4028/www.scientific.net/amr.510.536.

Full text

Abstract:

The nonlinear dynamics model of gearing system is developed based on RV transmission system. The influence of the nonlinear factors as time-varying meshing stiffness, backlash of the gear pairs and errors is considered. By means of the Lagrange equation the multi-degree-of-freedom differential equations of motion are derived. The differential equations are very hard to solve for which are characterized by positive semi-definition, time-variation and backlash-type nonlinearity. And linear and nonlinear restoring force are coexist in the equations. In order to solve easily, the differential equations are transformed to identical dimensionless nonlinear differential equations in matrix form. The establishment of the nonlinear differential equations laid a foundation for The Solution of differential equations and the analysis of the nonlinearity characteristics.

APA, Harvard, Vancouver, ISO, and other styles

11

Assanova, A. T., and Ye Shynarbek. "THE PARAMETER IDENTIFICATION PROBLEM FOR SYSTEM OF DIFFERENTIAL EQUATIONS." BULLETIN Series of Physics & Mathematical Sciences 73, no. 1 (2021): 7–13. http://dx.doi.org/10.51889/2021-1.1728-7901.01.

Full text

Abstract:

In this paper, the parameter identification problem for system of ordinary differential equations is considered. The parameter identification problem for system of ordinary differential equations is investigated by the Dzhumabaev’s parametrization method. At first, conditions for a unique solvability of the parameter identification problem for system of ordinary differential equations are obtained in the term of fundamental matrix of system’s differential part. Further, we establish conditions for a unique solvability of the parameter identification problem for system of ordinary differential equations in the terms of initial data. Algorithm for finding of approximate solution to a unique solvability of the parameter identification problem for system of ordinary differential equations is proposed and the conditions for its convergence are setted. Results this paper can be use for investigating of various problems with parameter and control problems for system of ordinary differential equations. The approach in this paper can be apply to the parameter identification problems for partial differential equations.

APA, Harvard, Vancouver, ISO, and other styles

12

Kaunda, Modify A. E. "Semi-closed-form solutions of the van der Pol oscillator system." E3S Web of Conferences 505 (2024): 03015. http://dx.doi.org/10.1051/e3sconf/202450503015.

Full text

Abstract:

Second order vector-valued nonlinear differential equations occurring in science and engineering have been considered which generally do not have closed-form solutions. Explicit incremental semi-analytical numerical solution procedures for nonlinear multiple-degree-of-freedom systems have been developed. Higher order equivalent differential equations were formulated and then subsequent values of vectors were updated using explicit Taylor series expansions. As the time-step tends to zero, the values of displacement and velocity are exact in the Taylor series expansions involving as many higher order derivatives as necessary. A typical second order differential equation considered was, the van der Pol oscillator. Further developments consisted of closed-form solutions of the van der Pol equation. What remains to be determined is the closed-form solution of displacement, which is being addressed. Further applications of the semi-analytical procedures to time-dependent systems should also include, time-independent equations that are differentiable in terms of other independent variables, such as partial differential equations that have many independent variables.

APA, Harvard, Vancouver, ISO, and other styles

13

Liu, Yang, and Kai Sun. "Solving Power System Differential Algebraic Equations Using Differential Transformation." IEEE Transactions on Power Systems 35, no. 3 (2020): 2289–99. http://dx.doi.org/10.1109/tpwrs.2019.2945512.

Full text

APA, Harvard, Vancouver, ISO, and other styles

14

Zlatanovska, Biljana, and Donc̆o Dimovski. "A modified Lorenz system: Definition and solution." Asian-European Journal of Mathematics 13, no. 08 (2020): 2050164. http://dx.doi.org/10.1142/s1793557120501648.

Full text

Abstract:

Based on the approximations of the Lorenz system of differential equations from the papers [B. Zlatanovska and D. Dimovski, Systems of difference equations approximating the Lorentz system of differential equations, Contributions Sec. Math. Tech. Sci. Manu. XXXIII 1–2 (2012) 75–96, B. Zlatanovska and D. Dimovski, Systems of difference equations as a model for the Lorentz system, in Proc. 5th Int. Scientific Conf. FMNS, Vol. I (Blagoevgrad, Bulgaria, 2013), pp. 102–107, B. Zlatanovska, Approximation for the solutions of Lorenz system with systems of differential equations, Bull. Math. 41(1) (2017) 51–61], we define a Modified Lorenz system, that is a local approximation of the Lorenz system. It is a system of three differential equations, the first two are the same as the first two of the Lorenz system, and the third one is a homogeneous linear differential equation of fifth order with constant coefficients. The solution of this system is based on the results from [D. Dimitrovski and M. Mijatovic, A New Approach to the Theory of Ordinary Differential Equations (Numerus, Skopje, 1995), pp. 23–33].

APA, Harvard, Vancouver, ISO, and other styles

15

Minglibayev, M. Zh, and A. B. Kosherbayeva. "DIFFERENTIAL EQUATIONS OF PLANETARY SYSTEMS." REPORTS 2, no. 330 (2020): 14–20. http://dx.doi.org/10.32014/10.32014/2020.2518-1483.26.

Full text

Abstract:

In this article will be considered many spherical bodies problem with variable masses, varying non-isotropic at different rates as celestial-mechanical model of non-stationary planetary systems. In this article were obtained differential equations of motions of spherical bodies with variable masses to reach purpose exploration of evolution planetary systems. The scientific importance of the work is exploration to the effects of masses’ variability of the dynamic evolution of the planetary system for a long period of time. According to equation of Mescherskiy, we obtained differential equations of motions of planetary systems in the absolute coordinates system and the relative coordinates system. On the basis of obtained differential equations in the relative coordinates system, we derived equations of motions in osculating elements in form of Lagrange's equations and canonically equations in osculating analogs second systems of Poincare's elements on the base aperiodic motion over the quasi-canonical cross- section.

APA, Harvard, Vancouver, ISO, and other styles

16

Kosek, Zdeněk. "Nonlinear boundary value problem for a system of nonlinear ordinary differential equations." Časopis pro pěstování matematiky 110, no. 2 (1985): 130–44. http://dx.doi.org/10.21136/cpm.1985.108595.

Full text

APA, Harvard, Vancouver, ISO, and other styles

17

Bartušek, Miroslav. "On oscillatory solutions of the system of differential equations with deviating arguments." Czechoslovak Mathematical Journal 35, no. 4 (1985): 529–32. http://dx.doi.org/10.21136/cmj.1985.102046.

Full text

APA, Harvard, Vancouver, ISO, and other styles

18

Tchaban, Vasyl, and Taras Ryzhyi. "Algebraic-differential equations of a nonlinear pass-through quadripole." Computational Problems of Electrical Engineering 13, no. 1 (2023): 35–38. http://dx.doi.org/10.23939/jcpee2023.01.035.

Full text

Abstract:

A method of forming algebraic-differential equations of a nonlinear pass-through active quadripole, which connect its independent pole currents and independent polar voltages, is proposed. The difficulty of the analysis lies in the fact that some of both internal and external unknowns may be under the symbol of differentiation. The common differential equations of the system of internal and external currents and voltages act as starting information for this formation. The method is demonstrated on two cases of the formation of corresponding algebraic-differential equations of systems as formed by nonlinear two-port elements. The analysis is significantly simplified in the case of internal D-degeneracies of the system or purely resistive circuits.

APA, Harvard, Vancouver, ISO, and other styles

19

Yamaleev, Robert M. "Generalized System of Riccati-Type Equations." EPJ Web of Conferences 173 (2018): 02019. http://dx.doi.org/10.1051/epjconf/201817302019.

Full text

Abstract:

A new system of generalized Riccati-type equations is derived. An interconnection between the solutions of n-th order differential equations and the solutions of a generalized system of Riccati-type equations is established. Inverse mapping from the solutions of generalized Riccati-type equations onto the linearly independent solutions of the n-th order differential equation is constructed.

APA, Harvard, Vancouver, ISO, and other styles

20

Jovovic, Ivana. "Differential transcendence of solutions of systems of linear differential equations based on total reduction of the system." Applicable Analysis and Discrete Mathematics, no. 00 (2020): 24. http://dx.doi.org/10.2298/aadm190627024j.

Full text

Abstract:

In this paper we consider total reduction of the nonhomogeneous linear system of operator equations with constant coefficients and commuting operators. The totally reduced system obtained in this manner is completely decoupled. All equations of the system differ only in the variables and in the nonhomogeneous terms. The homogeneous parts are obtained using the generalized characteristic polynomial of the system matrix. We also indicate how this technique may be used to examine differential transcendence of the solution of the linear system of the differential equations with constant coefficients over the complex field and meromorphic free terms.

APA, Harvard, Vancouver, ISO, and other styles

21

Et. al., Mridula Purohit,. "Solving Coupled Fractional Differential Equations Using Differential Transform Method." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 4 (2021): 535–39. http://dx.doi.org/10.17762/turcomat.v12i4.535.

Full text

Abstract:

This paper presents the solution of coupled equations which are of fractional order using differential transform method. In this paper we extend the scope of differential transform method to system of fractional differential equations so that we get the analytical solutions. The coupled fractional differential equations of a physical system, namely, coupled fractional oscillator with some applications is given via differential transform method. Here we introduce the solution of coupled oscillation of equal fractional order which can be enhanced to unequal fractional order.

APA, Harvard, Vancouver, ISO, and other styles

22

Zadorozhniy, V. G., and G. S. Tikhomirov. "On a system of differential equations with random parameters." Contemporary Mathematics. Fundamental Directions 68, no. 4 (2022): 621–34. http://dx.doi.org/10.22363/2413-3639-2022-68-4-621-634.

Full text

Abstract:

An explicit formula for the mathematical expectation and second moment functions of a solution to a linear system of ordinary differential equations with a random parameter and a vector random righthand side is obtained. The problem is reduced to the deterministic Cauchy problem for systems of first-order linear partial differential equations. We obtain an explicit formula for a solution of linear systems of partial differential equations of the first order with constant coeffcients. An example is given showing that random factors can have a stabilizing effect on a linear system of differential equations.

APA, Harvard, Vancouver, ISO, and other styles

23

Aldibekov, T. М., and M. M. Aldazharova. "On a linear system of differential equations." Journal of Mathematics, Mechanics and Computer Science 101, no. 1 (2019): 3–13. http://dx.doi.org/10.26577/jmmcs-2019-1-615.

Full text

APA, Harvard, Vancouver, ISO, and other styles

24

Pongérard, Patrice. "NONLINEAR SYSTEM OF SINGULAR PARTIAL DIFFERENTIAL EQUATIONS." Journal of Mathematical Sciences: Advances and Applications 43 (January 10, 2017): 31–53. http://dx.doi.org/10.18642/jmsaa_7100121748.

Full text

APA, Harvard, Vancouver, ISO, and other styles

25

Kutsenko, G. V., and L. I. Turchaninova. "Solving a special system of differential equations." Journal of Soviet Mathematics 66, no. 3 (1993): 2323–26. http://dx.doi.org/10.1007/bf01229604.

Full text

APA, Harvard, Vancouver, ISO, and other styles

26

Ding, Zuohua, Hui Shen, and Qi-Wei Ge. "Checking system boundedness using ordinary differential equations." Information Sciences 187 (March 2012): 245–65. http://dx.doi.org/10.1016/j.ins.2011.10.018.

Full text

APA, Harvard, Vancouver, ISO, and other styles

27

Bainov, D. D., A. B. Dishliev, and I. M. Stamova. "Asymptotic equivalence of a linear system of impulsive differential equations and a system of impulsive differential-difference equations." ANNALI DELL UNIVERSITA DI FERRARA 41, no. 1 (1995): 45–54. http://dx.doi.org/10.1007/bf02826007.

Full text

APA, Harvard, Vancouver, ISO, and other styles

28

Kádár, Fanni, and Gábor Stépán. "An implicit system of delay differential algebraic equations from hydrodynamics." Electronic Journal of Qualitative Theory of Differential Equations, no. 28 (2023): 1–8. http://dx.doi.org/10.14232/ejqtde.2023.1.28.

Full text

Abstract:

Direct spring operated pressure relief valves connected to a constantly charged vessel and a downstream pipe have a complex dynamics. The vessel-valve subsystem is described with an autonomous system of ordinary differential equations, while the presence of the pipe adds two partial differential equations to the mathematical model. The partial differential equations are transformed to a delay algebraic equation coupled to the ordinary differential equations. Due to a square root nonlinearity, the system is implicit. The linearized system can be transformed to a standard system of neutral delay differential equations (NDDEs) having more elaborated literature than the delay algebraic equations. First, the different forms of the mathematical model are presented, then the transformation of the linearized system is conducted. The paper aims at introducing this unusual mathematical model of an engineering system and inducing research focusing on the methodology to carry out bifurcation analysis in implicit NDDEs.

APA, Harvard, Vancouver, ISO, and other styles

29

Makarov, O., and I. Nikolenko. "Two-point boundary value problem for systems of pseudo-differential equations under boundary conditions containing pseudo-differential operators." V. N. Karazin Kharkiv National University. Ser. Mathematics, Applied Mathematics and Mechanics, no. 95 (June 18, 2022): 31–38. http://dx.doi.org/10.26565/2221-5646-2022-95-03.

Full text

Abstract:

This paper deals with a two-point boundary value problem for pseudodifferential equations and for systems of second order pseudodifferential equations under boundary conditions containing pseudodifferential operators. The need to consider pseudodifferential operators is caused by two reasons, first, such equations appear more and more often in applied problems, and second, by considering such equations, it is possible to achieve the well-posedness of the boundary value problem in the Schwartz space S and in its dual space.First, we consider a scalar pseudodifferential equation with a symbol belonging to the space $C_{-\infty}^{\infty}$, consists of infinitely differentiable functions of polinomial growth. For this equation it is found of the boundary condition under which a specific type the boundary value problem is well-posed in the space S. In addition, an example of a differential-difference equation and a specific boundary condition with a convolution-type pseudo-differential operator under which this boundary value problem is well-posed in the space S are given.Then we consider a system of two pseudodifferential equations with symbols from the space $C _ {-\infty} ^ {\infty}$. For this system, we prove the existence of a well posed boundary value problem in the space S. The Fourier transform and the reduction of the system to a triangular form are used in the proof. In this case, we also give an example of a system and a specific boundary condition under which this boundary value problem is correct in the space S.Thus, the work proves that for any pseudo-differential equation, as well as for a system of two pseudo-differential equations, there is always a correct boundary value problem in the $S$ space, while the boundary conditions contain pseudo-differential operators. The algorithm for constructing correct boundary conditions is also indicated. They are pseudo-differential operators whose symbols depend on the symbols of pseudo-differential equations.

APA, Harvard, Vancouver, ISO, and other styles

30

Assanova, Anar, and Zhanibek Tokmurzin. "A NONLOCAL MULTIPOINT PROBLEM FOR A SYSTEM OF FOURTH-ORDER PARTIAL DIFFERENTIAL EQUATIONS." Eurasian Mathematical Journal 11, no. 3 (2020): 8–20. http://dx.doi.org/10.32523/2077-9879-2020-11-3-08-20.

Full text

APA, Harvard, Vancouver, ISO, and other styles

31

Diblík, Josef. "The singular Cauchy-Nicoletti problem for the system of two ordinary differential equations." Mathematica Bohemica 117, no. 1 (1992): 55–67. http://dx.doi.org/10.21136/mb.1992.126234.

Full text

APA, Harvard, Vancouver, ISO, and other styles

32

AZIZ-ALAOUI, M. A. "DIFFERENTIAL EQUATIONS WITH MULTISPIRAL ATTRACTORS." International Journal of Bifurcation and Chaos 09, no. 06 (1999): 1009–39. http://dx.doi.org/10.1142/s0218127499000729.

Full text

Abstract:

A system of nonautonomous differential equations having Chua's piecewise-linearity is studied. A brief discussion about equilibrium points and their stability is given. It is also extended to obtain a system showing "multispiral" strange attractors, and some of the fundamental routes to "multispiral chaos" and bifurcation phenomena are demonstrated with various examples. The same work is done for other systems of autonomous or nonautonomous differential equations. This is achieved by modifying Chua's piecewise-linearity in order to have additional segments. The evolution of the dynamics and a mechanism for the development of multispiral strange attractors are discussed.

APA, Harvard, Vancouver, ISO, and other styles

33

Hilal, Khalid, and Ahmed Kajouni. "Existence of the Solution for System of Coupled Hybrid Differential Equations with Fractional Order and Nonlocal Conditions." International Journal of Differential Equations 2016 (2016): 1–9. http://dx.doi.org/10.1155/2016/4726526.

Full text

Abstract:

This paper is motivated by some papers treating the fractional hybrid differential equations with nonlocal conditions and the system of coupled hybrid fractional differential equations; an existence theorem for fractional hybrid differential equations involving Caputo differential operators of order1<α≤2is proved under mixed Lipschitz and Carathéodory conditions. The existence and uniqueness result is elaborated for the system of coupled hybrid fractional differential equations.

APA, Harvard, Vancouver, ISO, and other styles

34

Tokibetov, Zh A., N. E. Bashar, and А. К. Pirmanova. "THE CAUCHY-DIRICHLET PROBLEM FOR A SYSTEM OF FIRST-ORDER EQUATIONS." BULLETIN Series of Physics & Mathematical Sciences 72, no. 4 (2020): 68–72. http://dx.doi.org/10.51889/2020-4.1728-7901.10.

Full text

Abstract:

For a single second-order elliptic partial differential equation with sufficiently smooth coefficients, all classical boundary value problems that are correct for the Laplace equations are Fredholm. The formulation of classical boundary value problems for the laplace equation is dictated by physical applications. The simplest of the boundary value problems for the Laplace equation is the Dirichlet problem, which is reduced to the problem of the field of charges distributed on a certain surface. The Dirichlet problem for partial differential equations in space is usually called the Cauchy-Dirichlet problem. This work dedicated to systems of first-order partial differential equations of elliptic and hyperbolic types consisting of four equations with three unknown variables. An explicit solution of the CauchyDirichlet problem is constructed using the method of an exponential – differential operator. Giving a very simple example of the co-solution of the Cauchy problem for a second-order differential equation and the Cauchy problem for systems of first-order hyperbolic differential equations.

APA, Harvard, Vancouver, ISO, and other styles

35

Dontsova, Marina. "The nonlocal solvability conditions for a system with constant terms and coefficients of the variable t." Journal of Mathematics, Mechanics and Computer Science 122, no. 2 (2024): 27–35. http://dx.doi.org/10.26577/jmmcs2024-122-02-b3.

Full text

Abstract:

We consider the Cauchy problem for a system of quasilinear differential equations with constantterms and coefficients of the variablet.We investigate the solvability of the Cauchy problem fora system of quasilinear differential equations with constant terms and coefficients of the variabletusing the additional argument method. A theorem on the existence and uniqueness of the localsolution of the Cauchy problem for a system of quasilinear differential equations with constantterms and coefficients of the variabletis formulated. We obtain sufficient conditions for theexistence and uniqueness of a nonlocal solution of the Cauchy problem in original coordinates fora system of quasilinear differential equations with constant terms and coefficients of the variablet.A theorem on the existence and uniqueness of the nonlocal solution of the Cauchy problem fora system of quasilinear differential equations with constant terms and coefficients of the variabletis formulated. A theorem on the existence and uniqueness of the nonlocal solution of the Cauchyproblem for a system of quasilinear differential equations with constant terms and coefficients ofthe variabletis proved. The proof of the nonlocal solvability of the Cauchy problem for a systemof quasilinear differential equations with constant terms and coefficients of the variabletrelies onglobal estimates.

APA, Harvard, Vancouver, ISO, and other styles

36

Jain, Pankaj, Chandrani Basu, and Vivek Panwar. "Reduced $pq$-Differential Transform Method and Applications." Journal of Inequalities and Special Functions 13, no. 1 (2022): 24–40. http://dx.doi.org/10.54379/jiasf-2022-1-3.

Full text

Abstract:

In this paper, Reduced Differential Transform method in the framework of (p, q)-calculus, denoted by Rp,qDT , has been introduced and applied in solving a variety of differential equations such as diffusion equation, 2Dwave equation, K-dV equation, Burgers equations and Ito system. While the diffusion equation has been studied for the special case p = 1, i.e., in the framework of q-calculus, the other equations have not been studied even in q-calculus.

APA, Harvard, Vancouver, ISO, and other styles

37

Yuldashev, T. K. "О нелокальной краевой задаче для интегро-дифференциального уравнения в частных производных с вырожденным ядром". Владикавказский математический журнал, № 2 (22 червня 2022): 130–41. http://dx.doi.org/10.46698/h5012-2008-4560-g.

Full text

Abstract:

On a nonlocal boundary value problem for a partial integro-differential equations with degenerate kernel\Abstracteng{In this article the problems of the unique classical solvability and theconstruction of the solution of a nonlinear boundary value problem for a fifth orderpartial integro-differential equations with degenerate kernel are studied. Dirichletboundary conditions are specified with respect to the spatial variable. So, the Fourierseries method, based on the separation of variables is used. A countable system of~thesecond order ordinary integro-differential equations with degenerate kernel is obtained.The method of degenerate kernel is applied to this countable system of ordinaryintegro-differential equations. A system of~countable systems of algebraic equations isderived. Then the countable system of nonlinear Fredholm integral equations is obtained.Iteration process of solving this integral equation is constructed. Sufficient coefficientconditions of the unique solvability of the countable system of nonlinear integralequations are established for the regular values of parameter. In proof of uniquesolvability of the obtained countable system of nonlinear integral equations the method ofsuccessive approximations in combination with the contraction mapping method is used.In the proof of the convergence of Fourier series the Cauchy--Schwarz and Besselinequalities are applied. The smoothness of solution of the boundary value problemis also proved.

APA, Harvard, Vancouver, ISO, and other styles

38

Leibov, Roman. "Piecewise continuous approach to nonlinear differential equations approximation problem of computational structural mechanics." MATEC Web of Conferences 251 (2018): 04024. http://dx.doi.org/10.1051/matecconf/201825104024.

Full text

Abstract:

This paper presents a nonlinear differential equations system piecewise continuous approximation. The piecewise continuous approximation improves piecewise linear approximation through reducing the errors at the boundaries of different linear differential equations systems areas. The matrices of piecewise continuous differential and algebraic equations systems are estimated using nonlinear differential equations system time responses and random search method. The results of proposed approach application are presented.

APA, Harvard, Vancouver, ISO, and other styles

39

Kadirbayeva, Zh M., E. A. Bakirova, A. Sh Dauletbayeva, and A. A. Kassymgali. "AN ALGORITHM FOR SOLVING A BOUNDARY VALUE PROBLEM FOR ESSENTIALLY LOADED DIFFERENTIAL EQUATIONS." PHYSICO-MATHEMATICAL SERIES 2, no. 336 (2021): 6–14. http://dx.doi.org/10.32014/2021.2518-1726.15.

Full text

Abstract:

A linear boundary value problem for essentially loaded differential equations is considered. Using the properties of essentially loaded differential we reduce the considering problem to a two-point boundary value problem for loaded differential equations. This problem is investigated by parameterization method. We offer algorithm for solving to boundary value problem for the system of loaded differential equations. This algorithm includes of the numerical solving of the Cauchy problems for system of the ordinary differential equations and solving of the linear system of algebraic equations. For numerical solving of the Cauchy problem we apply the Runge–Kutta method of 4th order. The proposed numerical implementation is illustrated by example.

APA, Harvard, Vancouver, ISO, and other styles

40

Wong, E., and J. W. Zu. "Dynamic Response of a Coupled Spinning Timoshenko Shaft System." Journal of Vibration and Acoustics 121, no. 1 (1999): 110–13. http://dx.doi.org/10.1115/1.2893936.

Full text

Abstract:

The dynamic behavior of a simply-supported spinning Timoshenko shaft with coupled bending and torsion is analyzed. This is accomplished by transforming the set of nonlinear partial differential equations of motion into a set of linear ordinary differential equations. This set of ordinary differential equations is a time-varying system and the solution is obtained analytically in terms of Chebyshev series. A beating phenomoenon is observed from the numerical simulations, which is not observed for shaft systems where only bending vibration is considered.

APA, Harvard, Vancouver, ISO, and other styles

41

Wang, Wenli, and Junyan Bao. "Existence Results for Nonlinear Impulsive System with Causal Operators." Mathematics 12, no. 17 (2024): 2755. http://dx.doi.org/10.3390/math12172755.

Full text

Abstract:

In this paper, we establish sufficient conditions for some existence results for nonlinear impulsive differential equations involving causal operators. Our method is based on the monotone iterative technique, a new differential inequality, and the Schauder fixed point theorem. Moreover, we consider three impulsive differential equations as applications to verify our theoretical results.

APA, Harvard, Vancouver, ISO, and other styles

42

Căruțașu, Vasile. "Determining a Particular Solution for the Systems of Linear Differential Equations with Constant Coefficients." International conference KNOWLEDGE-BASED ORGANIZATION 23, no. 3 (2017): 30–36. http://dx.doi.org/10.1515/kbo-2017-0152.

Full text

Abstract:

Abstract As with the n-th order linear differential equations with constant coefficients, the problem to be solved is related to determining a particular solution, and then, using the general solution of the attached homogeneous system of linear differential equations with constant coefficients, to write the general solution of the initially given system. For homogeneous systems of linear differential equations with constant coefficients, the determination of the general solution is the method of eliminating or reducing which make the system a linear differential equation of the same order as that of the system, and its methods of solving it applies or the method of own values and vectors. If the system is non-homogeneous, then we also have to determine a particular solution that can be done in the same way as in the case of n-th order differential equations with constant coefficients, if the method of reduction or elimination was used, or the method of variation of constants, regardless of the method used to determine the general solution of the attached homogenous system of linear differential equations with constant coefficients. Whichever method is used, determining a particular solution for a system of linear differential equations with constant coefficients is difficult, in this study being proposed a method similar to that of n-th order linear differential equations with constant coefficients.

APA, Harvard, Vancouver, ISO, and other styles

43

Ivanov, Gennadiy G., Gennadiy V. Alferov, and Vladimir S. Korolev. "The Differential Equations Linear Homogeneous System Solutions Investigation." Вестник Пермского университета. Математика. Механика. Информатика, no. 1 (60) (2023): 47–53. http://dx.doi.org/10.17072/1993-0550-2023-1-47-53.

Full text

Abstract:

The paper shows that the fundamental zero-normalized solution of a linear homogeneous differ-ential equations system can be represented as an exponential matrices products formal series. If the system satisfies the equations system triangulation Perron theorem conditions, then the system solution can be represented as an exponential matrices finite product. In addition, an exponential matrix function differentiating formula is derived. Also, the transformation constructing problem is considered. Such, a homogeneous differential equations system allows to reduce to a triangular form.

APA, Harvard, Vancouver, ISO, and other styles

44

Kılıçman, Adem, and Wasan Ajeel Ahmood. "On matrix fractional differential equations." Advances in Mechanical Engineering 9, no. 1 (2017): 168781401668335. http://dx.doi.org/10.1177/1687814016683359.

Full text

Abstract:

The aim of this article is to study the matrix fractional differential equations and to find the exact solution for system of matrix fractional differential equations in terms of Riemann–Liouville using Laplace transform method and convolution product to the Riemann–Liouville fractional of matrices. Also, we show the theorem of non-homogeneous matrix fractional partial differential equation with some illustrative examples to demonstrate the effectiveness of the new methodology. The main objective of this article is to discuss the Laplace transform method based on operational matrices of fractional derivatives for solving several kinds of linear fractional differential equations. Moreover, we present the operational matrices of fractional derivatives with Laplace transform in many applications of various engineering systems as control system. We present the analytical technique for solving fractional-order, multi-term fractional differential equation. In other words, we propose an efficient algorithm for solving fractional matrix equation.

APA, Harvard, Vancouver, ISO, and other styles

45

Assanova, A. T., and Zh S. Tokmurzin. "Method of functional parametrization for solving a semi-periodic initial problem for fourth-order partial differential equations." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 100, no. 4 (2020): 5–16. http://dx.doi.org/10.31489/2020m4/5-16.

Full text

Abstract:

A semi-periodic initial boundary-value problem for a fourth-order system of partial differential equations is considered. Using the method of functional parametrization, an additional parameter is carried out and the studied problem is reduced to the equivalent semi-periodic problem for a system of integro-differential equations of hyperbolic type second order with functional parameters and integral relations. An interrelation between the semi-periodic problem for the system of integro-differential equations of hyperbolic type and a family of Cauchy problems for a system of ordinary differential equations is established. Algorithms for finding of solutions to an equivalent problem are constructed and their convergence is proved. Sufficient conditions of a unique solvability to the semi-periodic initial boundary value problem for the fourth-order system of partial differential equations are obtained.

APA, Harvard, Vancouver, ISO, and other styles

46

Tian, Baodan, Yanhong Qiu, and Yucai Ding. "Impulsive Control Strategy for a Nonautonomous Food-Chain System with Multiple Delays." Journal of Control Science and Engineering 2016 (2016): 1–9. http://dx.doi.org/10.1155/2016/6126545.

Full text

Abstract:

A nonautonomous food-chain system with Holling II functional response is studied, in which multiple delays of digestion are also considered. By applying techniques in differential inequalities, comparison theorem in ordinary differential equations, impulsive differential equations, and functional differential equations, some effective control strategies are obtained for the permanence of the system. Furthermore, effects of some important coefficients and delays on the permanence of the system are intuitively and clearly shown by series of numerical examples.

APA, Harvard, Vancouver, ISO, and other styles

47

Perev, Kamen. "SYSTEM CHARACTERISTICS OF DISTRIBUTED PARAMETER SYSTEMS." Proceedings of the Technical University of Sofia 70, no. 3 (2020): 34–44. http://dx.doi.org/10.47978/tus.2020.70.03.018.

Full text

Abstract:

The paper considers the problem of distributed parameter systems modeling. The basic model types are presented, depending on the partial differential equation, which determines the physical processes dynamics. The similarities and the differences with the models described in terms of ordinary differential equations are discussed. A special attention is paid to the problem of heat flow in a rod. The problem set up is demonstrated and the methods of its solution are discussed. The main characteristics from a system point of view are presented, namely the Green function and the transfer function. Different special cases for these characteristics are discussed, depending on the specific partial differential equation, as well as the initial conditions and the boundary conditions.

APA, Harvard, Vancouver, ISO, and other styles

48

Kandala, Shanti S., Surya Samukham, Thomas K. Uchida, and C. P. Vyasarayani. "Spurious roots of delay differential equations using Galerkin approximations." Journal of Vibration and Control 26, no. 15-16 (2020): 1178–84. http://dx.doi.org/10.1177/1077546319894172.

Full text

Abstract:

The dynamics of time-delay systems are governed by delay differential equations, which are infinite dimensional and can pose computational challenges. Several methods have been proposed for studying the stability characteristics of delay differential equations. One such method employs Galerkin approximations to convert delay differential equations into partial differential equations with boundary conditions; the partial differential equations are then converted into systems of ordinary differential equations, whereupon standard ordinary differential equation methods can be applied. The Galerkin approximation method can be applied to a second-order delay differential equation in two ways: either by converting into a second-order partial differential equation and then into a system of second-order ordinary differential equations (the “second-order Galerkin” method) or by first expressing as two first-order delay differential equations and converting into a system of first-order partial differential equations and then into a first-order ordinary differential equation system (the “first-order Galerkin” method). In this paper, we demonstrate that these subtly different formulation procedures lead to different roots of the characteristic polynomial. In particular, the second-order Galerkin method produces spurious roots near the origin, which must then be identified through substitution into the characteristic polynomial of the original delay differential equation. However, spurious roots do not arise if the first-order Galerkin method is used, which can reduce computation time and simplify stability analyses. We describe these two formulation strategies and present numerical examples to highlight their important differences.

APA, Harvard, Vancouver, ISO, and other styles

49

Zadorozhniy, V. G., and L. Yu Kabantsova. "On Solution of First-Order Linear Systems of Partial Differential Equations." Contemporary Mathematics. Fundamental Directions 67, no. 3 (2021): 549–63. http://dx.doi.org/10.22363/2413-3639-2021-67-3-549-563.

Full text

Abstract:

Explicit formulas for the first-order partial differential equations system solving were obtained. Solution found for the system with initial conditions. Calculation examples establishing statements truth mentioned. Searching for partial differential equations system solution mathematical expectation became more difficult issue as partial differential equations system with random processes coefficients were covered. Gaussian coefficients and uniformly distributed random process cases examples has been reviewed.

APA, Harvard, Vancouver, ISO, and other styles

50

El-kady, M., and M. A. Ibrahim. "Ultraspherical Differentiation Method for Solving System of Initial Value Differential Algebraic Equations." Computational Methods in Applied Mathematics 9, no. 3 (2009): 226–37. http://dx.doi.org/10.2478/cmam-2009-0014.

Full text

Abstract:

AbstractIn this paper, we introduce a new spectral method based on ultraspherical polynomials for solving systems of initial value differential algebraic equations. Moreover, the suggested method is applicable for a wide range of differential equations. The method is based on a new investigation of the ultraspherical spectral differentiation matrix to approximate the differential expressions in equations. The produced equations lead to algebraic systems and are converted to nonlinear programming. Numerical examples illustrate the robustness, accuracy, and efficiency of the proposed method.

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!