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Relevant bibliographies by topics / Nonlinear systems of equations

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Academic literature on the topic 'Nonlinear systems of equations'

Author: Grafiati

Published: 10 March 2023

Last updated: 13 June 2025

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Journal articles on the topic "Nonlinear systems of equations"

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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Nonlinear systems of equations"

1

Hadad, Yaron. "Integrable Nonlinear Relativistic Equations." Diss., The University of Arizona, 2013. http://hdl.handle.net/10150/293490.

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This work focuses on three nonlinear relativistic equations: the symmetric Chiral field equation, Einstein's field equation for metrics with two commuting Killing vectors and Einstein's field equation for diagonal metrics that depend on three variables. The symmetric Chiral field equation is studied using the Zakharov-Mikhailov transform, with which its infinitely many local conservation laws are derived and its solitons on diagonal backgrounds are studied. It is also proven that it is equivalent to a novel equation that poses a fascinating similarity to the Sinh-Gordon equation. For the 1+1 Einstein equation the Belinski-Zakharov transformation is explored. It is used to derive explicit formula for N gravitational solitons on arbitrary diagonal background. In particular, the method is used to derive gravitational solitons on the Einstein-Rosen background. The similarities and differences between the attributes of the solitons of the symmetric Chiral field equation and those of the 1+1 Einstein equation are emphasized, and their origin is pointed out. For the 1+2 Einstein equation, new equations describing diagonal metrics are derived and their compatibility is proven. Different gravitational waves are studied that naturally extend the class of Bondi-Pirani-Robinson waves. It is further shown that the Bondi-Pirani-Robinson waves are stable with respect to perturbations of the spacetime. Their stability is closely related to the stability of the Schwarzschild black hole and the relation between the two allows to conjecture about the stability of a wide range of gravitational phenomena. Lastly, a new set of equations that describe weak gravitational waves is derived. This new system of equations is closely and fundamentally connected with the nonlinear Schrödinger equation and can be properly called the nonlinear Schrödinger-Einstein equations. A few preliminary solutions are constructed.

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Zerihun, Tadesse G. "Nonlinear Techniques for Stochastic Systems of Differential Equations." Scholar Commons, 2013. http://scholarcommons.usf.edu/etd/4970.

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Two of the most well-known nonlinear methods for investigating nonlinear dynamic processes in sciences and engineering are nonlinear variation of constants parameters and comparison method. Knowing the existence of solution process, these methods provide a very powerful tools for investigating variety of problems, for example, qualitative and quantitative properties of solutions, finding error estimates between solution processes of stochastic system and the corresponding nominal system, and inputs for the designing engineering and industrial problems. The aim of this work is to systematically develop mathematical tools to undertake the mathematical frame-work to investigate a complex nonlinear nonstationary stochastic systems of differential equations. A complex nonlinear nonstationary stochastic system of differential equations are decomposed into nonlinear systems of stochastic perturbed and unperturbed differential equations. Using this type of decomposition, the fundamental properties of solutions of nonlinear stochastic unperturbed systems of differential equations are investigated(1). The fundamental properties are used to find the representation of solution process of nonlinear stochastic complex perturbed system in terms of solution process of nonlinear stochastic unperturbed system(2). Employing energy function method and the fundamental properties of It\^{o}-Doob type stochastic auxiliary system of differential equations, we establish generalized variation of constants formula for solution process of perturbed stochastic system of differential equations(3). Results regarding deviation of solution of perturbed system with respect to solution of nominal system of stochastic differential equations are developed(4). The obtained results are used to study the qualitative properties of perturbed stochastic system of differential equations(5). Examples are given to illustrate the usefulness of the results. Employing energy function method and the fundamental properties of It\^{o}-Doob type stochastic auxiliary system of differential equations, we establish generalized variational comparison theorems in the context of stochastic and deterministic differential for solution processes of perturbed stochastic system of differential equations(6). Results regarding deviation of solutions with respect to nominal stochastic system are also developed(7). The obtained results are used to study the qualitative properties of perturbed stochastic system(8). Examples are given to illustrate the usefulness of the results. A simple dynamical model of the effect of radiant flux density and CO_2 concentration on the rate of photosynthesis in light, dark and enzyme reactions are analyzed(9). The coupled system of dynamic equations are solved numerically for some values of rate constant and radiant flux density. We used Matlab to solve the system numerically. Moreover, with the assumption that dynamic model of CO_2 concentration is studied.

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Jaschke, Leonhard. "Preconditioned Arnoldi methods for systems of nonlinear equations /." Paris (121 Av. des Champs-Élysées, 75008) : Wiku, 2004. http://catalogue.bnf.fr/ark:/12148/cb391991990.

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Foley, Dawn Christine. "Applications of State space realization of nonlinear input/output difference equations." Thesis, Georgia Institute of Technology, 1999. http://hdl.handle.net/1853/16818.

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Van, der Walt Jan Harm. "Generalized solutions of systems of nonlinear partial differential equations." Thesis, Pretoria : [s.n.], 2009. http://upetd.up.ac.za/thesis/available/etd-05242009-122628.

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Reichelt, Sina. "Two-scale homogenization of systems of nonlinear parabolic equations." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät, 2015. http://dx.doi.org/10.18452/17385.

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Ziel dieser Arbeit ist es zwei verschiedene Klassen von Systemen nichtlinearer parabolischer Gleichungen zu homogenisieren, und zwar Reaktions-Diffusions-Systeme mit verschiedenen Diffusionslängenskalen und Gleichungen vom Typ Cahn-Hilliard. Wir betrachten parabolische Gleichungen mit periodischen Koeffizienten, wobei die Periode dem Verhältnis der charakteristischen mikroskopischen zu der makroskopische Längenskala entspricht. Unser Ziel ist es, effektive Gleichungen rigoros herzuleiten, um die betrachteten Systeme besser zu verstehen und den Simulationsaufwand zu minimieren. Wir suchen also einen Konvergenzbegriff, mit dem die Lösung des Ausgangsmodells im Limes der Periode gegen Null gegen die Lösung des effektiven Modells konvergiert. Um die periodische Mikrostruktur und die verschiedenen Diffusivitäten zu erfassen, verwenden wir die Zwei-Skalen Konvergenz mittels periodischer Auffaltung. Der erste Teil der Arbeit handelt von Reaktions-Diffusions-Systemen, in denen einige Spezies mit der charakteristischen Diffusionslänge der makroskopischen Skala und andere mit der mikroskopischen diffundieren. Die verschiedenen Diffusivitäten führen zu einem Verlust der Kompaktheit, sodass wir nicht direkt den Grenzwert der nichtlinearen Terme bestimmen können. Wir beweisen mittels starker Zwei-Skalen Konvergenz, dass das effektive Modell ein zwei-skaliges Modell ist, welches von der makroskopischen und der mikroskopischen Skale abhängt. Unsere Methode erlaubt es uns, explizite Raten für die Konvergenz der Lösungen zu bestimmen. Im zweiten Teil betrachten wir Gleichungen vom Typ Cahn-Hilliard, welche ortsabhängige Mobilitätskoeffizienten und allgemeine Potentiale beinhalten. Wir beweisen evolutionäre Gamma-Konvergenz der zugehörigen Gradientensysteme basierend auf der Gamma-Konvergenz der Energien und der Dissipationspotentiale.<br>The aim of this thesis is to derive homogenization results for two different types of systems of nonlinear parabolic equations, namely reaction-diffusion systems involving different diffusion length scales and Cahn-Hilliard-type equations. The coefficient functions of the considered parabolic equations are periodically oscillating with a period which is proportional to the ratio between the charactersitic microscopic and macroscopic length scales. In view of greater structural insight and less computational effort, it is our aim to rigorously derive effective equations as the period tends to zero such that solutions of the original model converge to solutions of the effective model. To account for the periodic microstructure as well as for the different diffusion length scales, we employ the method of two-scale convergence via periodic unfolding. In the first part of the thesis, we consider reaction-diffusion systems, where for some species the diffusion length scale is of order of the macroscopic length scale and for other species it is of order of the microscopic one. Based on the notion of strong two-scale convergence, we prove that the effective model is a two-scale reaction-diffusion system depending on the macroscopic and the microscopic scale. Our approach supplies explicit rates for the convergence of the solution. In the second part, we consider Cahn-Hilliard-type equations with position-dependent mobilities and general potentials. It is well-known that the classical Cahn-Hilliard equation admits a gradient structure. Based on the Gamma-convergence of the energies and the dissipation potentials, we prove evolutionary Gamma-convergence, for the associated gradient system such that we obtain in the limit of vanishing periods a Cahn-Hilliard equation with homogenized coefficients.

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Alam, Md Shafiful. "Iterative Methods to Solve Systems of Nonlinear Algebraic Equations." TopSCHOLAR®, 2018. https://digitalcommons.wku.edu/theses/2305.

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Iterative methods have been a very important area of study in numerical analysis since the inception of computational science. Their use ranges from solving algebraic equations to systems of differential equations and many more. In this thesis, we discuss several iterative methods, however our main focus is Newton's method. We present a detailed study of Newton's method, its order of convergence and the asymptotic error constant when solving problems of various types as well as analyze several pitfalls, which can affect convergence. We also pose some necessary and sufficient conditions on the function f for higher order of convergence. Different acceleration techniques are discussed with analysis of the asymptotic behavior of the iterates. Analogies between single variable and multivariable problems are detailed. We also explore some interesting phenomena while analyzing Newton's method for complex variables.

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Handel, Andreas. "Limits of Localized Control in Extended Nonlinear Systems." Diss., Georgia Institute of Technology, 2004. http://hdl.handle.net/1853/5025.

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We investigate the limits of localized linear control in spatially extended, nonlinear systems. Spatially extended, nonlinear systems can be found in virtually every field of engineering and science. An important category of such systems are fluid flows. Fluid flows play an important role in many commercial applications, for instance in the chemical, pharmaceutical and food-processing industries. Other important fluid flows include air- or water flows around cars, planes or ships. In all these systems, it is highly desirable to control the flow of the respective fluid. For instance control of the air flow around an airplane or car leads to better fuel-economy and reduced noise production. Usually, it is impossible to apply control everywhere. Consider an airplane: It would not be feasibly to cover the whole body of the plane with control units. Instead, one can place the control units at localized regions, such as points along the edge of the wings, spaced as far apart from each other as possible. These considerations lead to an important question: For a given system, what is the minimum number of localized controllers that still ensures successful control? Too few controllers will not achieve control, while using too many leads to unnecessary expenses and wastes resources. To answer this question, we study localized control in a class of model equations. These model equations are good representations of many real fluid flows. Using these equations, we show how one can design localized control that renders the system stable. We study the properties of the control and derive several expressions that allow us to determine the limits of successful control. We show how the number of controllers that are needed for successful control depends on the size and type of the system, as well as the way control is implemented. We find that especially the nonlinearities and the amount of noise present in the system play a crucial role. This analysis allows us to determine under which circumstances a given number of controllers can successfully stabilize a given system.

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9

Twiton, Michael. "Analysis of Singular Solutions of Certain Painlevé Equations." Thesis, The University of Sydney, 2018. http://hdl.handle.net/2123/18206.

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The six Painlevé equations can be described as the boundary between the non- integrable- and the trivially integrable-systems. Ever since their discovery they have found numerous applications in mathematics and physics. The solutions of the Painlevé equations are, in most cases, highly transcendental and hence cannot be expressed in closed form. Asymptotic methods do better, and can establish the behaviour of some of the solutions of the Painlevé equations in the neighbourhood of a singularity, such as the point at infinity. Although the quantitative nature of these neighbourhoods is not initially implied from the asymptotic analysis, some regularity results exist for some of the Painlevé equations. In this research, we will present such results for some of the remaining Painlevé equations. In particular, we will provide concrete estimates of the intervals of analyticity of a one-parameter family of solutions of the second Painlevé equation, and estimate the domain of analyticity of a “triply-truncated” solution of the fourth Painlevé equation. In addition we will also deduce the existence of solutions with particular asymptotic behaviour for the discrete Painlevé equations, which are discrete integrable nonlinear systems.

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Liu, Weian, Yin Yang, and Gang Lu. "Viscosity solutions of fully nonlinear parabolic systems." Universität Potsdam, 2002. http://opus.kobv.de/ubp/volltexte/2008/2621/.

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In this paper, we discuss the viscosity solutions of the weakly coupled systems of fully nonlinear second order degenerate parabolic equations and their Cauchy-Dirichlet problem. We prove the existence, uniqueness and continuity of viscosity solution by combining Perron's method with the technique of coupled solutions. The results here generalize those in [2] and [3].

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Books on the topic "Nonlinear systems of equations"

1

Drazin, P. G. Nonlinear systems. Cambridge University Press, 1992.

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2

Drazin, P. G. Nonlinear systems. Cambridge University Press, 1992.

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3

Nonlinear systems analysis. 2nd ed. Prentice Hall, 1993.

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Liu, Wu-Ming, and Emmanuel Kengne. Schrödinger Equations in Nonlinear Systems. Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-6581-2.

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Adomian, G. Nonlinear stochastic operator equations. Academic Press, 1986.

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Verhulst, F. Nonlinear differential equations and dynamical systems. Springer-Verlag, 1990.

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Verhulst, Ferdinand. Nonlinear Differential Equations and Dynamical Systems. Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-642-97149-5.

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Verhulst, Ferdinand. Nonlinear Differential Equations and Dynamical Systems. Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-642-61453-8.

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Leung, Anthony W. Systems of Nonlinear Partial Differential Equations. Springer Netherlands, 1989. http://dx.doi.org/10.1007/978-94-015-3937-1.

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Makhankov, Vladimir G., and Oktay K. Pashaev, eds. Nonlinear Evolution Equations and Dynamical Systems. Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-76172-0.

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Book chapters on the topic "Nonlinear systems of equations"

1

Gilbert, Robert P., George C. Hsiao, and Robert J. Ronkese. "Nonlinear Autonomous Systems." In Differential Equations, 2nd ed. Chapman and Hall/CRC, 2021. http://dx.doi.org/10.1201/9781003175643-9.

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Marchuk, Guri I. "Nonlinear Equations." In Adjoint Equations and Analysis of Complex Systems. Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-017-0621-6_4.

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Pommaret, J. F. "Nonlinear Systems." In Partial Differential Equations and Group Theory. Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-017-2539-2_4.

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Sauvigny, Friedrich. "Nonlinear Elliptic Systems." In Partial Differential Equations 2. Springer London, 2012. http://dx.doi.org/10.1007/978-1-4471-2984-4_6.

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Goodwine, Bill. "Introduction to Nonlinear Systems." In Engineering Differential Equations. Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-7919-3_13.

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Klein, Christian, and Jean-Claude Saut. "Davey–Stewartson and Related Systems." In Nonlinear Dispersive Equations. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-91427-1_4.

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Shaikhet, Leonid. "Nonlinear Systems." In Lyapunov Functionals and Stability of Stochastic Difference Equations. Springer London, 2011. http://dx.doi.org/10.1007/978-0-85729-685-6_7.

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Stoyan, Gisbert, and Agnes Baran. "Nonlinear Equations and Systems." In Compact Textbooks in Mathematics. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-44660-8_7.

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Andrei, Neculai. "Nonlinear Systems of Equations." In Nonlinear Optimization Applications Using the GAMS Technology. Springer US, 2013. http://dx.doi.org/10.1007/978-1-4614-6797-7_4.

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Floudas, Christodoulos A., Pãnos M. Pardalos, Claire S. Adjiman, et al. "Nonlinear Systems of Equations." In Nonconvex Optimization and Its Applications. Springer US, 1999. http://dx.doi.org/10.1007/978-1-4757-3040-1_14.

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Conference papers on the topic "Nonlinear systems of equations"

1

Tselishcheva, Anastasiia A., and Konstantin K. Semenov. "Metrological Approach to Solve Nonlinear Equations and Systems of Nonlinear Equations." In 2021 XXIV International Conference on Soft Computing and Measurements (SCM). IEEE, 2021. http://dx.doi.org/10.1109/scm52931.2021.9507196.

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Vladimirov, Andrei G., Vladislav Y. Toronov, and Vladimir L. Derbov. "Complex Lorenz equations." In Nonlinear Dynamics of Laser and Optical Systems, edited by Valery V. Tuchin. SPIE, 1997. http://dx.doi.org/10.1117/12.276193.

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Etrich, C., Paul Mandel, and Kenju Otsuka. "Laser rate equations with phase-sensitive interactions." In Nonlinear Dynamics in Optical Systems. Optica Publishing Group, 1992. http://dx.doi.org/10.1364/nldos.1992.tuc7.

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We derive the following set of equations describing a two-mode semiconductor laser for the case of a Fabry-Perot configuration, taking into account the holes burned into the amplifying medium by the standing field pattern and phase-sensitive interactions: (1) where κ = κ2/κ1 is the ratio of the decay rates of the electric fields E1 and E2. It is fixed to be larger than unity.

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Makhankov, Vladimir, Igor Puzynin, and Oktay Pashaev. "Nonlinear Evolution Equations and Dynamical Systems." In 8th International Workshop (NEEDS '92). WORLD SCIENTIFIC, 1993. http://dx.doi.org/10.1142/9789814535601.

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Boiti, M., L. Martina, and F. Pempinelli. "Nonlinear Evolution Equations and Dynamical Systems." In Workshop (NEEDS '91). WORLD SCIENTIFIC, 1992. http://dx.doi.org/10.1142/9789814538114.

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Arkhipova, Arina. "New a priori estimates for nondiagonal strongly nonlinear parabolic systems." In Parabolic and Navier–Stokes equations. Institute of Mathematics Polish Academy of Sciences, 2008. http://dx.doi.org/10.4064/bc81-0-1.

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Ta-Tsien, Li. "Nonlinear Evolution Equations and Infinite-Dimensional Dynamical Systems." In Conference on Nonlinear Evolution Equations and Infinite-Dimensional Dynamical Systems. WORLD SCIENTIFIC, 1997. http://dx.doi.org/10.1142/9789814530019.

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Glad, T., and J. Sjoberg. "Hamilton-Jacobi equations for nonlinear descriptor systems." In 2006 American Control Conference. IEEE, 2006. http://dx.doi.org/10.1109/acc.2006.1655494.

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Jafari, Raheleh, and Wen Yu. "Uncertainty Nonlinear Systems Control with Fuzzy Equations." In 2015 IEEE International Conference on Systems, Man, and Cybernetics (SMC). IEEE, 2015. http://dx.doi.org/10.1109/smc.2015.502.

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Jafari, Raheleh, and Wen Yu. "Uncertainty Nonlinear Systems Modeling with Fuzzy Equations." In 2015 IEEE International Conference on Information Reuse and Integration (IRI). IEEE, 2015. http://dx.doi.org/10.1109/iri.2015.36.

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Reports on the topic "Nonlinear systems of equations"

1

Seidman, Thomas I. Nonlinear Systems of Partial Differential Equations. Defense Technical Information Center, 1989. http://dx.doi.org/10.21236/ada217581.

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2

Hale, Jack, Constantine M. Dafermos, John Mallet-Paret, Panagiotis E. Souganidis, and Walter Strauss. Dynamical Systems and Nonlinear Partial Differential Equations. Defense Technical Information Center, 1989. http://dx.doi.org/10.21236/ada255356.

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Dafermos, Constantine M., John Mallet-Paret, Panagiotis E. Souganidis, and Walter Strauss. Dynamical Systems and Nonlinear Partial Differential Equations. Defense Technical Information Center, 1993. http://dx.doi.org/10.21236/ada271514.

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Shearer, Michael. Systems of Nonlinear Hyperbolic Partial Differential Equations. Defense Technical Information Center, 1997. http://dx.doi.org/10.21236/ada344449.

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Schnabel, Robert B., and Paul D. Frank. Solving Systems of Nonlinear Equations by Tensor Methods. Defense Technical Information Center, 1986. http://dx.doi.org/10.21236/ada169927.

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Bouaricha, A., and R. B. Schnabel. Tensor methods for large sparse systems of nonlinear equations. Office of Scientific and Technical Information (OSTI), 1996. http://dx.doi.org/10.2172/434848.

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Zhang, Xiaodong, Richard H. Byrd, and Robert B. Schnabel. Parallel Methods for Solving Nonlinear Block Bordered Systems of Equations. Defense Technical Information Center, 1989. http://dx.doi.org/10.21236/ada217062.

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Bader, Brett William. Tensor-Krylov methods for solving large-scale systems of nonlinear equations. Office of Scientific and Technical Information (OSTI), 2004. http://dx.doi.org/10.2172/919158.

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Li, Guangye. The Secant/Finite Difference Algorithm for Solving Sparse Nonlinear Systems of Equations. Defense Technical Information Center, 1986. http://dx.doi.org/10.21236/ada453093.

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Bouaricha, A., and R. B. Schnabel. TENSOLVE: A software package for solving systems of nonlinear equations and nonlinear least squares problems using tensor methods. Office of Scientific and Technical Information (OSTI), 1996. http://dx.doi.org/10.2172/435303.

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