Articles de revues : « Nonlinear systems of equations »

1

Jan, Jiří. « Recursive algorithms for solving systems of nonlinear equations ». Applications of Mathematics 34, n^o 1 (1989) : 33–45. http://dx.doi.org/10.21136/am.1989.104332.

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2

Friedman, Avner, et Jindrich Necas. « Systems of nonlinear wave equations with nonlinear viscosity ». Pacific Journal of Mathematics 135, n^o 1 (1 novembre 1988) : 29–55. http://dx.doi.org/10.2140/pjm.1988.135.29.

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3

Tamizhmani, K. M., J. Satsuma, B. Grammaticos et A. Ramani. « Nonlinear integrodifferential equations as discrete systems ». Inverse Problems 15, n^o 3 (1 janvier 1999) : 787–91. http://dx.doi.org/10.1088/0266-5611/15/3/310.

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4

Ramos, J. I. « Nonlinear diferrential equations and dynamical systems ». Applied Mathematical Modelling 16, n^o 2 (février 1992) : 108. http://dx.doi.org/10.1016/0307-904x(92)90092-h.

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5

Boichuk, O. A., et I. A. Golovats’ka. « Weakly Nonlinear Systems of Integrodifferential Equations ». Journal of Mathematical Sciences 201, n^o 3 (2 août 2014) : 288–95. http://dx.doi.org/10.1007/s10958-014-1989-6.

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van der Laan, Gerard, Dolf Talman et Zaifu Yang. « Solving discrete systems of nonlinear equations ». European Journal of Operational Research 214, n^o 3 (novembre 2011) : 493–500. http://dx.doi.org/10.1016/j.ejor.2011.05.024.

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Batt, Jürgen, et Carlo Cercignani. « Nonlinear equations in many-particle systems ». Transport Theory and Statistical Physics 26, n^o 7 (janvier 1997) : 827–38. http://dx.doi.org/10.1080/00411459708224424.

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8

Adomian, G. « Systems of nonlinear partial differential equations ». Journal of Mathematical Analysis and Applications 115, n^o 1 (avril 1986) : 235–38. http://dx.doi.org/10.1016/0022-247x(86)90038-7.

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9

Fife, Paul C. « Systems of nonlinear partial differential equations ». Mathematical Biosciences 79, n^o 1 (mai 1986) : 119–20. http://dx.doi.org/10.1016/0025-5564(86)90022-2.

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10

Aisha Rafi, Aisha Rafi. « Homotopy Perturbation Method for Solving Systems of Linear and Nonlinear Kolmogorov Equations ». International Journal of Scientific Research 2, n^o 3 (1 juin 2012) : 290–92. http://dx.doi.org/10.15373/22778179/mar2013/89.

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11

Elaydi, Hatem, et Mohammed Elamassie. « Multi-rate Ripple-Free Deadbeat Control for Nonlinear Systems Using Diophantine Equations ». International Journal of Engineering and Technology 4, n^o 4 (2012) : 489–94. http://dx.doi.org/10.7763/ijet.2012.v4.417.

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12

Kosek, Zdeněk. « Nonlinear boundary value problem for a system of nonlinear ordinary differential equations ». Časopis pro pěstování matematiky 110, n^o 2 (1985) : 130–44. http://dx.doi.org/10.21136/cpm.1985.108595.

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13

BILYI, Leonid, Oleh POLISHCHUK, Svitlana LISEVICH, Anatoly ZALIZETSKY et 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, n^o 3 (26 mai 2022) : 99–103. http://dx.doi.org/10.31891/2307-5732-2022-309-3-99-103.

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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.

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14

Engibaryan, N. B., et L. G. Arabadzhyan. « SYSTEMS OF WIENER-HOPF INTEGRAL EQUATIONS, AND NONLINEAR FACTORIZATION EQUATIONS ». Mathematics of the USSR-Sbornik 52, n^o 1 (28 février 1985) : 181–208. http://dx.doi.org/10.1070/sm1985v052n01abeh002884.

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15

Forster, W. « Some computational methods for systems of nonlinear equations and systems of polynomial equations ». Journal of Global Optimization 2, n^o 4 (1992) : 317–56. http://dx.doi.org/10.1007/bf00122427.

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16

Korpusov, M. O. « Blowup of solutions of nonlinear equations and systems of nonlinear equations in wave theory ». Theoretical and Mathematical Physics 174, n^o 3 (mars 2013) : 307–14. http://dx.doi.org/10.1007/s11232-013-0028-y.

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17

Hribar, Mary Beth, Eugene L. Allgower et Kurt Georg. « Computational Solutions of Nonlinear Systems of Equations. » Mathematics of Computation 62, n^o 206 (avril 1994) : 943. http://dx.doi.org/10.2307/2153556.

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18

Cushing, J. M. « Periodically forced nonlinear systems of difference equations ». Journal of Difference Equations and Applications 3, n^o 5-6 (janvier 1998) : 487–513. http://dx.doi.org/10.1080/10236199708808120.

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19

Nataf, Jean-Michel. « Algorithm of simplification of nonlinear equations systems ». ACM SIGSAM Bulletin 26, n^o 3 (août 1992) : 9–16. http://dx.doi.org/10.1145/141897.141905.

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20

Rashidinia, Jalil, et Ali Tahmasebi. « Systems of nonlinear Volterra integro-differential equations ». Numerical Algorithms 59, n^o 2 (14 juillet 2011) : 197–212. http://dx.doi.org/10.1007/s11075-011-9484-3.

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21

Loghin, D., D. Ruiz et A. Touhami. « Adaptive preconditioners for nonlinear systems of equations ». Journal of Computational and Applied Mathematics 189, n^o 1-2 (mai 2006) : 362–74. http://dx.doi.org/10.1016/j.cam.2005.04.060.

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22

Jing, Kang, et Qu Chang-Zheng. « Linearization of Systems of Nonlinear Diffusion Equations ». Chinese Physics Letters 24, n^o 9 (23 août 2007) : 2467–70. http://dx.doi.org/10.1088/0256-307x/24/9/002.

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23

Berg, Lothar. « Overdetermined Systems of Nonlinear Partial Differential Equations ». Zeitschrift für Analysis und ihre Anwendungen 8, n^o 6 (1989) : 571–75. http://dx.doi.org/10.4171/zaa/376.

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24

Fushchych, W. I., et R. M. Cherniha. « Galilei-invariant nonlinear systems of evolution equations ». Journal of Physics A : Mathematical and General 28, n^o 19 (7 octobre 1995) : 5569–79. http://dx.doi.org/10.1088/0305-4470/28/19/012.

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25

Bykov, V. I., A. M. Kytmanov et S. G. Myslivets. « Power sums of nonlinear systems of equations ». Doklady Mathematics 76, n^o 2 (octobre 2007) : 641–44. http://dx.doi.org/10.1134/s1064562407050018.

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26

Schittkowski, K. « Parameter estimation in systems of nonlinear equations ». Numerische Mathematik 68, n^o 1 (1 juin 1994) : 129–42. http://dx.doi.org/10.1007/s002110050052.

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27

Medina, Rigoberto. « Perturbations of Nonlinear Systems of Difference Equations ». Journal of Mathematical Analysis and Applications 204, n^o 2 (décembre 1996) : 545–53. http://dx.doi.org/10.1006/jmaa.1996.0453.

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28

Shen, Y. Q., et T. J. Ypma. « Solving nonlinear systems of equations with only one nonlinear variable ». Journal of Computational and Applied Mathematics 30, n^o 2 (mai 1990) : 235–46. http://dx.doi.org/10.1016/0377-0427(90)90031-t.

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29

Fofana, M. S. « Dimensional reduction of nonlinear time delay systems ». International Journal of Mathematics and Mathematical Sciences 2005, n^o 2 (2005) : 311–28. http://dx.doi.org/10.1155/ijmms.2005.311.

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Whenever there is a time delay in a dynamical system, the study of stability becomes an infinite-dimensional problem. The centre manifold theorem, together with the classical Hopf bifurcation, is the most valuable approach for simplifying the infinite-dimensional problem without the assumption of small time delay. This dimensional reduction is illustrated in this paper with the delay versions of the Duffing and van der Pol equations. For both nonlinear delay equations, transcendental characteristic equations of linearized stability are examined through Hopf bifurcation. The infinite-dimensional nonlinear solutions of the delay equations are decomposed into stable and centre subspaces, whose respective dimensions are determined by the linearized stability of the transcendental equations. Linear semigroups, infinitesimal generators, and their adjoint forms with bilinear pairings are the additional candidates for the infinite-dimensional reduction.

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30

Lowe, G. K., et M. A. Zohdy. « Modeling nonlinear systems using multiple piecewise linear equations ». Nonlinear Analysis : Modelling and Control 15, n^o 4 (25 octobre 2010) : 451–58. http://dx.doi.org/10.15388/na.15.4.14317.

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This paper describes a technique for modeling nonlinear systems using multiple piecewise linear equations. The technique provides a means for linearizing the nonlinear system in such a way as to not limit the large signal behavior of the target system. The nonlinearity in the target system must be able to be represented as a piecewise linear function. A simple third order nonlinear system is used to demonstrate the technique. The behavior of the modeled system is compared to the behavior of the nonlinear system.

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31

Svarc, Ivan, et Radomil Matousek. « Contribution to Stability Control of Nonlinear Systems ». Advanced Materials Research 463-464 (février 2012) : 1579–82. http://dx.doi.org/10.4028/www.scientific.net/amr.463-464.1579.

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The most powerful methods of systems analysis have been developed for linear control systems. For a linear control system, all the relationships between the variables are linear differential equations, usually with constant coefficients. Actual control systems usually contain some nonlinear elements. In the following we show how the equations for nonlinear systems may be linearized. But the result is only applicable in a sufficiently small region in the neighbourhood of equilibrium point. The table in this paper includes the nonlinear equations and their the linear approximation. Then it is easy to find out if the nonlinear system is or is not stable; the task that usually ranks among the difficult tasks in engineering practice.

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32

Gaiduk, A. R. « Nonlinear Control Systems Design by Transformation Method ». Mekhatronika, Avtomatizatsiya, Upravlenie 19, n^o 12 (8 décembre 2018) : 755–61. http://dx.doi.org/10.17587/mau.19.755-761.

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The analytical approaches to design of nonlinear control systems by the transformation of the nonlinear plant equations into quasilinear forms or into Jordan controlled form are considered. Shortly definitions of these forms and the mathematical expressions necessary for design of the control systems by these methods are submitted. These approaches can be applied if the plant’s nonlinearities are differentiable, the plant is controllable and the additional conditions are satisfied. Procedure of a control system design, i.e. definition of the equations of the control device, in both cases is completely analytical. Desirable quality of transients is provided with that, that corresponding values are given to roots of the characteristic equations of some matrixes by calculation of the nonlinear control. The proposed methods provide asymptotical stability of the equilibrium in a bounded domain of the state space or its global stability and also desirable performance of transients. Performance of the nonlinear plants equations in the quasilinear form has no any complexities, if the mentioned above conditions are satisfied. The transformation of these equations to the Jordan controlled form very much often is reduced to change of the state variables designations of the plants. The suggested methods can be applied to design of control systems by various nonlinear technical plants ship-building, machine-building, aviation, agricultural and many other manufactures. Examples of the control systems design by the proposed analytical methods are given.

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33

Kimbrough, S. « Nonlinear Regulators for a Class of Decomposable Systems ». Journal of Dynamic Systems, Measurement, and Control 109, n^o 2 (1 juin 1987) : 128–32. http://dx.doi.org/10.1115/1.3143829.

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This paper presents nonlinear regulators for a large class of systems that includes many linear systems, bilinear systems, and variable structure systems. Membership in this class requires that the dynamic equations of a system decompose into a set of stable equations and into a set of equations which are nulled by some feasible control value. When the stable set of equations represents a linear system and the remaining set of equations is linear in the control variables (with other variables fixed), the resulting regulators become attractive alternatives to linear regulators. They have time invariant forms suitable for real-time control, have the capability to handle complicated constraints, and have control properties beyond the range of linear regulators. The procedure followed is to obtain a Lyapunov function for the stable set of equations, which is then used to assure closed loop stability. Sufficient conditions for maintaining Lyapunov stability are treated as constraints in optimizations that yield the control policies. These constraints can always be satisfied because it is assumed that some feasible control nulls the remaining set of equations. The benefits of this procedure are that stability can be obtained by working with a smaller more manageable set of equations than the full system equations and control policies can be obtained from readily solvable optimizations. Although the resulting nonlinear regulators are suboptimal their performance can often be bounded by the performance of an optimal linear regulator.

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Jafari, Raheleh, et Wen Yu. « Fuzzy Modeling for Uncertainty Nonlinear Systems with Fuzzy Equations ». Mathematical Problems in Engineering 2017 (2017) : 1–10. http://dx.doi.org/10.1155/2017/8594738.

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The uncertain nonlinear systems can be modeled with fuzzy equations by incorporating the fuzzy set theory. In this paper, the fuzzy equations are applied as the models for the uncertain nonlinear systems. The nonlinear modeling process is to find the coefficients of the fuzzy equations. We use the neural networks to approximate the coefficients of the fuzzy equations. The approximation theory for crisp models is extended into the fuzzy equation model. The upper bounds of the modeling errors are estimated. Numerical experiments along with comparisons demonstrate the excellent behavior of the proposed method.

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Pant, Sangeeta, Anuj Kumar et Mangey Ram. « Solution of Nonlinear Systems of Equations via Metaheuristics ». International Journal of Mathematical, Engineering and Management Sciences 4, n^o 5 (1 octobre 2019) : 1108–26. http://dx.doi.org/10.33889/10.33889/ijmems.2019.4.5-088.

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A framework devoted to the solution of nonlinear systems of equations using grey wolf optimization algorithm (GWO) and a multi-objective particle swarm optimization algorithm (MOPSO) is presented in this work. Due to several numerical issues and very high computational complexity, it is hard to find the solution of such a complex nonlinear system of equations. It then explains that the problem of solution to a system of nonlinear equations can be simplified by viewing it as an optimization problem and solutions can be obtained by applying a nature inspired optimization technique. The results achieved are compared with classical as well as new techniques established in the literature. The proposed framework also seems to be very effective for the problems of system of non-linear equations arising in the various fields of science. For this purpose, the problem of neurophysiology application and the problem of combustion of hydrocarbons are considered for testing. Empirical results show that the presented framework is bright to deal with the high dimensional equations system.

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Nadeem, Muhammad, et Fengquan Li. « He–Laplace method for nonlinear vibration systems and nonlinear wave equations ». Journal of Low Frequency Noise, Vibration and Active Control 38, n^o 3-4 (16 janvier 2019) : 1060–74. http://dx.doi.org/10.1177/1461348418818973.

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Savageau, Michael A., et Eberhard O. Voit. « Recasting nonlinear differential equations as S-systems : a canonical nonlinear form ». Mathematical Biosciences 87, n^o 1 (novembre 1987) : 83–115. http://dx.doi.org/10.1016/0025-5564(87)90035-6.

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38

Redkina, Zakinyan, Zakinyan, Surneva et Yanovskaya. « Bäcklund Transformations for Nonlinear Differential Equations and Systems ». Axioms 8, n^o 2 (11 avril 2019) : 45. http://dx.doi.org/10.3390/axioms8020045.

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In this work, new Bäcklund transformations (BTs) for generalized Liouville equations were obtained. Special cases of Liouville equations with exponential nonlinearity that have a multiplier that depends on the independent variables and first-order derivatives from the function were considered. Two- and three-dimensional cases were considered. The BTs construction is based on the method proposed by Clairin. The solutions of the considered equations have been found using the BTs, with a unified algorithm. In addition, the work develops the Clairin’s method for the system of two third-order equations related to the integrable perturbation and complexification of the Korteweg-de Vries (KdV) equation. Among the constructed BTs an analog of the Miura transformations was found. The Miura transformations transfer the initial system to that of perturbed modified KdV (mKdV) equations. It could be shown on this way that, considering the system as a link between the real and imaginary parts of a complex function, it is possible to go to the complexified KdV (cKdV) and here the analog of the Miura transformations transforms it into the complexification of the mKdV.

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Goncharenko, Borys, Larysa Vikhrova et Mariia Miroshnichenko. « Optimal control of nonlinear stationary systems at infinite control time ». Central Ukrainian Scientific Bulletin. Technical Sciences, n^o 4(35) (2021) : 88–93. http://dx.doi.org/10.32515/2664-262x.2021.4(35).88-93.

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The article presents a solution to the problem of control synthesis for dynamical systems described by linear differential equations that function in accordance with the integral-quadratic quality criterion under uncertainty. External perturbations, errors and initial conditions belong to a certain set of uncertainties. Therefore, the problem of finding the optimal control in the form of feedback on the output of the object is presented in the form of a minimum problem of optimal control under uncertainty. The problem of finding the optimal control and initial state, which maximizes the quality criterion, is considered in the framework of the optimization problem, which is solved by the method of Lagrange multipliers after the introduction of the auxiliary scalar function - Hamiltonian. The case of a stationary system on an infinite period of time is considered. The formulas that can be used for calculations are given for the first and second variations. It is proposed to solve the problem of control search in two stages: search of intermediate solution at fixed values of control and error vectors and subsequent search of final optimal control. The solution of -optimal control for infinite time taking into account the signal from the compensator output is also considered, as well as the solution of the corresponding matrix algebraic equations of Ricatti type.

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40

Stan, Andrei. « Nonlinear systems with a partial Nash type equilibrium ». Studia Universitatis Babes-Bolyai Matematica 66, n^o 2 (15 juin 2021) : 397–408. http://dx.doi.org/10.24193/subbmath.2021.2.14.

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"In this paper xed point arguments and a critical point technique are combined leading to hybrid existence results for a system of three operator equations where only two of the equations have a variational structure. The components of the solution which are associated to the equations having a variational form represent a Nash-type equilibrium of the corresponding energy functionals. The result is achieved by an iterative scheme based on Ekeland's variational principle."

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Tasbozan, Orkun, Yücel Çenesiz, Ali Kurt et Dumitru Baleanu. « New analytical solutions for conformable fractional PDEs arising in mathematical physics by exp-function method ». Open Physics 15, n^o 1 (10 novembre 2017) : 647–51. http://dx.doi.org/10.1515/phys-2017-0075.

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AbstractModelling of physical systems mathematically, produces nonlinear evolution equations. Most of the physical systems in nature are intrinsically nonlinear, therefore modelling such systems mathematically leads us to nonlinear evolution equations. The analysis of the wave solutions corresponding to the nonlinear partial differential equations (NPDEs), has a vital role for studying the nonlinear physical events. This article is written with the intention of finding the wave solutions of Nizhnik-Novikov-Veselov and Klein-Gordon equations. For this purpose, the exp-function method, which is based on a series of exponential functions, is employed as a tool. This method is an useful and suitable tool to obtain the analytical solutions of a considerable number of nonlinear FDEs within a conformable derivative.

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Zhanlav, T., Changbum Chun, Kh Otgondorj et V. Ulziibayar. « High-order iterations for systems of nonlinear equations ». International Journal of Computer Mathematics 97, n^o 8 (25 août 2019) : 1704–24. http://dx.doi.org/10.1080/00207160.2019.1652739.

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Gupta, D. K. « Enclosing the solutions of nonlinear systems of equations ». International Journal of Computer Mathematics 73, n^o 3 (janvier 2000) : 389–404. http://dx.doi.org/10.1080/00207160008804905.

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Qu, Changzheng. « Potential symmetries to systems of nonlinear diffusion equations ». Journal of Physics A : Mathematical and Theoretical 40, n^o 8 (6 février 2007) : 1757–73. http://dx.doi.org/10.1088/1751-8113/40/8/005.

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Szczepanik, Ewa, Alexey A. Tret’yakov et Eugene E. Tyrtyshnikov. « Solution method for underdetermined systems of nonlinear equations ». Russian Journal of Numerical Analysis and Mathematical Modelling 34, n^o 3 (26 juin 2019) : 163–74. http://dx.doi.org/10.1515/rnam-2019-0014.

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Abstract In this paper we present a new solution method for underdetermined systems of nonlinear equations in a neighborhood of a certain point of the variety of solutions where the Jacoby matrix has incomplete rank. Such systems are usually called degenerate. It is known that the Gauss–Newton method can be used in the degenerate case. However, the variety of solutions in a neighborhood of the considered point can have several branches in the degenerate case. Therefore, the analysis of convergence of the method requires special techniques based on the constructions of the theory of p-regularity and p-factor-operators.

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Grosan, C., et A. Abraham. « A New Approach for Solving Nonlinear Equations Systems ». IEEE Transactions on Systems, Man, and Cybernetics - Part A : Systems and Humans 38, n^o 3 (mai 2008) : 698–714. http://dx.doi.org/10.1109/tsmca.2008.918599.

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Kálovics, F. « An interval method for nonlinear systems of equations ». Applicationes Mathematicae 20, n^o 2 (1988) : 299–305. http://dx.doi.org/10.4064/am-20-2-299-305.

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Brown, Peter N., et Youcef Saad. « Hybrid Krylov Methods for Nonlinear Systems of Equations ». SIAM Journal on Scientific and Statistical Computing 11, n^o 3 (mai 1990) : 450–81. http://dx.doi.org/10.1137/0911026.

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Ahmad, B., M. S. Alhothuali, H. H. Alsulami, M. Kirane et S. Timoshin. « On Nonlinear Nonlocal Systems of Reaction Diffusion Equations ». Abstract and Applied Analysis 2014 (2014) : 1–6. http://dx.doi.org/10.1155/2014/804784.

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The reaction diffusion system with anomalous diffusion and a balance lawut+-Δα/2u=-fu,v, vt+-∆β/2v=fu,v,0<α,β<2, is con sidered. The existence of global solutions is proved in two situations: (i) a polynomial growth condition is imposed on the reaction termfwhen0<α≤β≤2; (ii) no growth condition is imposed on the reaction termfwhen0<β≤α≤2.

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Hirsch, Michael J., Panos M. Pardalos et Mauricio G. C. Resende. « Solving systems of nonlinear equations with continuous GRASP ». Nonlinear Analysis : Real World Applications 10, n^o 4 (août 2009) : 2000–2006. http://dx.doi.org/10.1016/j.nonrwa.2008.03.006.

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