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Journal articles on the topic 'Nonlinear systems of equations'

Author: Grafiati

Published: 10 March 2023

Last updated: 25 July 2025

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1

Jan, Jiří. "Recursive algorithms for solving systems of nonlinear equations." Applications of Mathematics 34, no. 1 (1989): 33–45. http://dx.doi.org/10.21136/am.1989.104332.

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2

Jahedi, Sana, Timothy Sauer, and James A. Yorke. "Structured Systems of Nonlinear Equations." SIAM Journal on Applied Mathematics 83, no. 4 (2023): 1696–716. http://dx.doi.org/10.1137/22m1529178.

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3

Friedman, Avner, and Jindrich Necas. "Systems of nonlinear wave equations with nonlinear viscosity." Pacific Journal of Mathematics 135, no. 1 (1988): 29–55. http://dx.doi.org/10.2140/pjm.1988.135.29.

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4

Tamizhmani, K. M., J. Satsuma, B. Grammaticos, and A. Ramani. "Nonlinear integrodifferential equations as discrete systems." Inverse Problems 15, no. 3 (1999): 787–91. http://dx.doi.org/10.1088/0266-5611/15/3/310.

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5

Ramos, J. I. "Nonlinear diferrential equations and dynamical systems." Applied Mathematical Modelling 16, no. 2 (1992): 108. http://dx.doi.org/10.1016/0307-904x(92)90092-h.

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6

Boichuk, O. A., and I. A. Golovats’ka. "Weakly Nonlinear Systems of Integrodifferential Equations." Journal of Mathematical Sciences 201, no. 3 (2014): 288–95. http://dx.doi.org/10.1007/s10958-014-1989-6.

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7

van der Laan, Gerard, Dolf Talman, and Zaifu Yang. "Solving discrete systems of nonlinear equations." European Journal of Operational Research 214, no. 3 (2011): 493–500. http://dx.doi.org/10.1016/j.ejor.2011.05.024.

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8

Batt, Jürgen, and Carlo Cercignani. "Nonlinear equations in many-particle systems." Transport Theory and Statistical Physics 26, no. 7 (1997): 827–38. http://dx.doi.org/10.1080/00411459708224424.

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9

Adomian, G. "Systems of nonlinear partial differential equations." Journal of Mathematical Analysis and Applications 115, no. 1 (1986): 235–38. http://dx.doi.org/10.1016/0022-247x(86)90038-7.

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10

Fife, Paul C. "Systems of nonlinear partial differential equations." Mathematical Biosciences 79, no. 1 (1986): 119–20. http://dx.doi.org/10.1016/0025-5564(86)90022-2.

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11

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.

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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

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12

Fofana, M. S. "Dimensional reduction of nonlinear time delay systems." International Journal of Mathematics and Mathematical Sciences 2005, no. 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-dimensiona

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13

Aisha Rafi, Aisha Rafi. "Homotopy Perturbation Method for Solving Systems of Linear and Nonlinear Kolmogorov Equations." International Journal of Scientific Research 2, no. 3 (2012): 290–92. http://dx.doi.org/10.15373/22778179/mar2013/89.

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14

Elaydi, Hatem, and Mohammed Elamassie. "Multi-rate Ripple-Free Deadbeat Control for Nonlinear Systems Using Diophantine Equations." International Journal of Engineering and Technology 4, no. 4 (2012): 489–94. http://dx.doi.org/10.7763/ijet.2012.v4.417.

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15

Mindasari, Eva, Sawaluddin Sawaluddin, and Parapat Gultom. "Comparison of Genetic Algorithm and Particle Swarm Optimization in Determining the Solution of Nonlinear System of Equations." sinkron 8, no. 3 (2024): 1600–1607. http://dx.doi.org/10.33395/sinkron.v8i3.13785.

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Nonlinear systems of equations often appear in various fields of science and engineering, but their analytical solutions are difficult to find, so numerical methods are needed to solve them. Optimization algorithms are very effective in finding solutions to nonlinear systems of equations especially when traditional analytical and numerical methods are difficult to apply. Two popular optimization methods used for this purpose are Genetic Algorithm (GA) and Particle Swarm Optimization (PSO). This study aims to compare the effectiveness of GA and PSO in finding solutions to nonlinear systems of e

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16

Svarc, Ivan, and Radomil Matousek. "Contribution to Stability Control of Nonlinear Systems." Advanced Materials Research 463-464 (February 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 ea

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17

Jafari, Raheleh, and 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 pr

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18

Tasbozan, Orkun, Yücel Çenesiz, Ali Kurt, and Dumitru Baleanu. "New analytical solutions for conformable fractional PDEs arising in mathematical physics by exp-function method." Open Physics 15, no. 1 (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

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19

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.

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20

Lowe, G. K., and M. A. Zohdy. "Modeling nonlinear systems using multiple piecewise linear equations." Nonlinear Analysis: Modelling and Control 15, no. 4 (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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21

Dewasurendra, Mangalagama, and Kuppalapalle Vajravelu. "On the Method of Inverse Mapping for Solutions of Coupled Systems of Nonlinear Differential Equations Arising in Nanofluid Flow, Heat and Mass Transfer." Applied Mathematics and Nonlinear Sciences 3, no. 1 (2018): 1–14. http://dx.doi.org/10.21042/amns.2018.1.00001.

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AbstractVery recently, Liao has invented a Directly Defining Inverse Mapping Method (MDDiM) for nonlinear differential equations. Liao’s method is novel and can be used for solving several problems arising in science and engineering, if we can extend it to nonlinear systems. Hence, in this paper, we extend Liao’s method to nonlinear-coupled systems of three differential equations. Our extension is not limited to single, double or triple equations, but can be applied to systems of any number of equations.

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22

Forster, W. "Some computational methods for systems of nonlinear equations and systems of polynomial equations." Journal of Global Optimization 2, no. 4 (1992): 317–56. http://dx.doi.org/10.1007/bf00122427.

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23

Engibaryan, N. B., and L. G. Arabadzhyan. "SYSTEMS OF WIENER-HOPF INTEGRAL EQUATIONS, AND NONLINEAR FACTORIZATION EQUATIONS." Mathematics of the USSR-Sbornik 52, no. 1 (1985): 181–208. http://dx.doi.org/10.1070/sm1985v052n01abeh002884.

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24

Korpusov, M. O. "Blowup of solutions of nonlinear equations and systems of nonlinear equations in wave theory." Theoretical and Mathematical Physics 174, no. 3 (2013): 307–14. http://dx.doi.org/10.1007/s11232-013-0028-y.

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25

Gaiduk, A. R. "Nonlinear Control Systems Design by Transformation Method." Mekhatronika, Avtomatizatsiya, Upravlenie 19, no. 12 (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 co

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26

Hribar, Mary Beth, Eugene L. Allgower, and Kurt Georg. "Computational Solutions of Nonlinear Systems of Equations." Mathematics of Computation 62, no. 206 (1994): 943. http://dx.doi.org/10.2307/2153556.

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27

Cushing, J. M. "Periodically forced nonlinear systems of difference equations." Journal of Difference Equations and Applications 3, no. 5-6 (1998): 487–513. http://dx.doi.org/10.1080/10236199708808120.

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28

Nataf, Jean-Michel. "Algorithm of simplification of nonlinear equations systems." ACM SIGSAM Bulletin 26, no. 3 (1992): 9–16. http://dx.doi.org/10.1145/141897.141905.

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29

Rashidinia, Jalil, and Ali Tahmasebi. "Systems of nonlinear Volterra integro-differential equations." Numerical Algorithms 59, no. 2 (2011): 197–212. http://dx.doi.org/10.1007/s11075-011-9484-3.

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30

Loghin, D., D. Ruiz, and A. Touhami. "Adaptive preconditioners for nonlinear systems of equations." Journal of Computational and Applied Mathematics 189, no. 1-2 (2006): 362–74. http://dx.doi.org/10.1016/j.cam.2005.04.060.

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31

Jing, Kang, and Qu Chang-Zheng. "Linearization of Systems of Nonlinear Diffusion Equations." Chinese Physics Letters 24, no. 9 (2007): 2467–70. http://dx.doi.org/10.1088/0256-307x/24/9/002.

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32

Berg, Lothar. "Overdetermined Systems of Nonlinear Partial Differential Equations." Zeitschrift für Analysis und ihre Anwendungen 8, no. 6 (1989): 571–75. http://dx.doi.org/10.4171/zaa/376.

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33

Fushchych, W. I., and R. M. Cherniha. "Galilei-invariant nonlinear systems of evolution equations." Journal of Physics A: Mathematical and General 28, no. 19 (1995): 5569–79. http://dx.doi.org/10.1088/0305-4470/28/19/012.

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34

Bykov, V. I., A. M. Kytmanov, and S. G. Myslivets. "Power sums of nonlinear systems of equations." Doklady Mathematics 76, no. 2 (2007): 641–44. http://dx.doi.org/10.1134/s1064562407050018.

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35

Schittkowski, K. "Parameter estimation in systems of nonlinear equations." Numerische Mathematik 68, no. 1 (1994): 129–42. http://dx.doi.org/10.1007/s002110050052.

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36

Medina, Rigoberto. "Perturbations of Nonlinear Systems of Difference Equations." Journal of Mathematical Analysis and Applications 204, no. 2 (1996): 545–53. http://dx.doi.org/10.1006/jmaa.1996.0453.

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37

Kimbrough, S. "Nonlinear Regulators for a Class of Decomposable Systems." Journal of Dynamic Systems, Measurement, and Control 109, no. 2 (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 i

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38

Shen, Y. Q., and T. J. Ypma. "Solving nonlinear systems of equations with only one nonlinear variable." Journal of Computational and Applied Mathematics 30, no. 2 (1990): 235–46. http://dx.doi.org/10.1016/0377-0427(90)90031-t.

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39

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.

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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

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40

Lee, Jong Gyu, Kazuhiko Terashima, and Sang Ryong Lee. "Derivement of Constraint Equations of Driving Motor for Rotary Crane Systems." International Journal of Modern Physics B 17, no. 08n09 (2003): 1976–82. http://dx.doi.org/10.1142/s0217979203019976.

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In this paper, the dynamical model of rotary crane systems becomes nonlinear state equations. These equations are obtained by nonlinear equations of motion which are derived from transfer function of driving motors and equations of motion for a load. From these state equations, Lyapunov function of rotary crane systems is derived from integral method. This function secures stability of autonomous rotary crane systems. Also Constraint equations of rotation motor, boom motor, and hoist motor are derived from this function.

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41

Fatimatuzzahra, Fatimatuzzahra, Aang Nuryaman, La Zakaria, and Agus Sutrisno. "SOLUTION OF FULLY FUZZY NONLINEAR EQUATION SYSTEMS USING GENETIC ALGORITHM." BAREKENG: Jurnal Ilmu Matematika dan Terapan 19, no. 2 (2025): 1169–78. https://doi.org/10.30598/barekengvol19iss2pp1169-1178.

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A system of nonlinear equations is a collection of several interrelated non-linear equations. Currently, systems of nonlinear equations are used not only on crisp but also on fuzzy numbers. A fuzzy number is an ordered pair function that has a degree of membership [0,1]. Meanwhile, a fully fuzzy system of equations is a system of equations that applies fuzzy number arithmetic operations. The solution of non-linear equation systems is usually complicated to solve analytically, so numerical methods are used as an alternative to solve these problems. In this research, the steps to find the soluti

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42

Shaikhet, Leonid. "Stability of the Exponential Type System of Stochastic Difference Equations." Mathematics 11, no. 18 (2023): 3975. http://dx.doi.org/10.3390/math11183975.

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The method of studying the stability in the probability for nonlinear systems of stochastic difference equations is demonstrated on two systems with exponential and fractional nonlinearities. The proposed method can be applied to nonlinear systems of higher dimensions and with other types of nonlinearity, both for difference equations and for differential equations with delay.

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43

Sözbir, Nedim. "A New Approach to the Simulation of Thermal Systems." Journal of Energy Resources Technology 128, no. 3 (2005): 161–67. http://dx.doi.org/10.1115/1.2213274.

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In this paper, thermal systems are simulated and analyzed with a new approach. Thermal system design equations can be obtained as a nonlinear algebraic equation system and then this nonlinear equation system is converted to a well-defined or non-well-defined linear equation system. The transformation of the nonlinear system equations to linear system equations is realized by using the first-order Taylor series expansion; after that, the linear system of equations of our thermal system is obtained. These linear equations are then solved by our new suggested approach. This new algorithm and conv

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44

Motsa, S. S., F. G. Awad, Z. G. Makukula, and P. Sibanda. "The Spectral Homotopy Analysis Method Extended to Systems of Partial Differential Equations." Abstract and Applied Analysis 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/241594.

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The spectral homotopy analysis method is extended to solutions of systems of nonlinear partial differential equations. The SHAM has previously been successfully used to find solutions of nonlinear ordinary differential equations. We solve the nonlinear system of partial differential equations that model the unsteady nonlinear convective flow caused by an impulsively stretching sheet. The numerical results generated using the spectral homotopy analysis method were compared with those found using the spectral quasilinearisation method (SQLM) and the two results were in good agreement.

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45

Jamil, Bismah, Tooba Feroze, and Muhammad Safdar. "Optimal systems and their group-invariant solutions to geodesic equations." International Journal of Geometric Methods in Modern Physics 16, no. 09 (2019): 1950135. http://dx.doi.org/10.1142/s0219887819501354.

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We find one-dimensional optimal systems of the Lie subalgebras of Noether symmetries associated with systems of geodesic equations. Further, we find invariants corresponding to each element of the derived optimal system. The derived invariants are shown to reduce systems of geodesic equations (nonlinear systems of quadratically semi-linear second-order ordinary differential equations (ODEs)) to nonlinear systems of first-order ODEs. The resulting systems are solved via known methods (e.g. separation of variables, integrating factor, etc.). In some cases, we provide exact solutions of these sys

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46

Abad, Manuel F., Alicia Cordero, and Juan R. Torregrosa. "Fourth- and Fifth-Order Methods for Solving Nonlinear Systems of Equations: An Application to the Global Positioning System." Abstract and Applied Analysis 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/586708.

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Two iterative methods of order four and five, respectively, are presented for solving nonlinear systems of equations. Numerical comparisons are made with other existing second- and fourth-order schemes to solve the nonlinear system of equations of theGlobal Positioning Systemand some academic nonlinear systems.

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47

Denier, J. P., and R. Grimshaw. "Slowly-varying bifurcation theory in dissipative systems." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 31, no. 3 (1990): 301–18. http://dx.doi.org/10.1017/s0334270000006664.

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AbstractSystems of coupled nonlinear differential equations with an externally controlled slowly-varying bifurcation parameter are considered. Canonical equations governing the transition between bifurcated solutions are derived by making use of methods of “steady” bifurcation theory. It is found that, depending on the initial amplitudes, the solutions of the transition equations are either asymptotically equivalent to the bifurcated solutions or the solutions develop algebraic singularities at some positive finite time. These singularities correspond to a transition to a solution of a fully n

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48

Pant, Sangeeta, Anuj Kumar, and Mangey Ram. "Solution of Nonlinear Systems of Equations via Metaheuristics." International Journal of Mathematical, Engineering and Management Sciences 4, no. 5 (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 a

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49

Shiau, Ting-Nung, and An-Nan Jean. "Prediction of Periodic Response of Flexible Mechanical Systems With Nonlinear Characteristics." Journal of Vibration and Acoustics 112, no. 4 (1990): 501–7. http://dx.doi.org/10.1115/1.2930135.

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A numerical-analytical method for the prediction of steady state periodic response of large order nonlinear rotordynamic systems is addressed. Using this method, the set of nonlinear differential equations governing the motion of the rotor systems is transformed to a set of nonlinear algebraic equations. A condensation technique is proposed to reduce the nonlinear algebraic equations to those only related to the physical coordinates associated with nonlinear components. The method allows for the inclusion of searching for sub, super, ultra-sub and ultra-super harmonic components of the system

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50

Stan, Andrei. "Nonlinear systems with a partial Nash type equilibrium." Studia Universitatis Babes-Bolyai Matematica 66, no. 2 (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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