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Books on the topic 'Difference equation system'

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Published: 11 March 2023

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1

Kikuchi, Tetsuya. Studies on commuting difference systems arising from solvable lattice models. Sendai, Japan: Tohoku University, 2000.

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2

Ahlbrandt, Calvin D. Discrete Hamiltonian systems: Difference equations, continued fractions, and Riccati equations. Dordrecht: Kluwer Academic Publishers, 1996.

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3

Bohner, Martin, Yiming Ding, and Ondřej Došlý, eds. Difference Equations, Discrete Dynamical Systems and Applications. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-24747-2.

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4

Alsedà i Soler, Lluís, Jim M. Cushing, Saber Elaydi, and Alberto A. Pinto, eds. Difference Equations, Discrete Dynamical Systems and Applications. Berlin, Heidelberg: Springer Berlin Heidelberg, 2016. http://dx.doi.org/10.1007/978-3-662-52927-0.

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5

Elaydi, Saber, Christian Pötzsche, and Adina Luminiţa Sasu, eds. Difference Equations, Discrete Dynamical Systems and Applications. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-20016-9.

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6

Arendt, Wolfgang, Joseph A. Ball, Jussi Behrndt, Karl-Heinz Förster, Volker Mehrmann, and Carsten Trunk, eds. Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations. Basel: Springer Basel, 2012. http://dx.doi.org/10.1007/978-3-0348-0297-0.

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7

Layton, Richard A. Principles of Analytical System Dynamics. New York, NY: Springer New York, 1998.

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8

Elaydi, Saber, Yoshihiro Hamaya, Hideaki Matsunaga, and Christian Pötzsche, eds. Advances in Difference Equations and Discrete Dynamical Systems. Singapore: Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-6409-8.

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9

Bohner, Martin, Stefan Siegmund, Roman Šimon Hilscher, and Petr Stehlík, eds. Difference Equations and Discrete Dynamical Systems with Applications. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-35502-9.

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10

Baigent, Steve, Martin Bohner, and Saber Elaydi, eds. Progress on Difference Equations and Discrete Dynamical Systems. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-60107-2.

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11

Orlando, Merino, ed. Discrete dynamical systems and difference equations with Mathematica. Boca Raton: Chapman & Hall/CRC, 2002.

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12

Lakshmikantham, V. Dynamic systems on measure chains. Dordrecht: Kluwer Academic Publishers, 1996.

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13

name, No. Advances in dynamic equations on time scales. Boston, MA: Birkhuser, 2003.

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14

1966-, Bohner Martin, and Peterson Allan C, eds. Advances in dynamic equations on time scales. Boston: Birkhäuser, 2003.

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15

Chambers, Marcus J. The estimation of systems of joint differential-difference equations. Colchester: Essex University, Department of Economics, 1995.

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16

Habib, Ammari, Capdeboscq Yves 1971-, and Kang Hyeonbae, eds. Multi-scale and high-contrast PDE: From modelling, to mathematical analysis, to inversion : Conference on Multi-scale and High-contrast PDE:from Modelling, to Mathematical Analysis, to Inversion, June 28-July 1, 2011, University of Oxford, United Kingdom. Providence, R.I: American Mathematical Society, 2010.

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17

Orlik, Lyubov', and Galina Zhukova. Operator equation and related questions of stability of differential equations. ru: INFRA-M Academic Publishing LLC., 2020. http://dx.doi.org/10.12737/1061676.

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The monograph is devoted to the application of methods of functional analysis to the problems of qualitative theory of differential equations. Describes an algorithm to bring the differential boundary value problem to an operator equation. The research of solutions to operator equations of special kind in the spaces polutoratonny with a cone, where the limitations of the elements of these spaces is understood as the comparability them with a fixed scale element of exponential type. Found representations of the solutions of operator equations in the form of contour integrals, theorems of existence and uniqueness of such solutions. The spectral criteria for boundedness of solutions of operator equations and, as a consequence, sufficient spectral features boundedness of solutions of differential and differential-difference equations in Banach space. The results obtained for operator equations with operators and work of Volterra operators, allowed to extend to some systems of partial differential equations known spectral stability criteria for solutions of A. M. Lyapunov and also to generalize theorems on the exponential characteristic. The results of the monograph may be useful in the study of linear mechanical and electrical systems, in problems of diffraction of electromagnetic waves, theory of automatic control, etc. It is intended for researchers, graduate students functional analysis and its applications to operator and differential equations.
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18

AlSharawi, Ziyad, Jim M. Cushing, and Saber Elaydi, eds. Theory and Applications of Difference Equations and Discrete Dynamical Systems. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-662-44140-4.

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19

Koçak, Hüseyin. Differential and difference equations through computer experiments: With diskettes containing PHASER, an animator/simulator for dynamical systems for IBM personal computers. 2nd ed. New York: Springer-Verlag, 1989.

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20

N, Elaydi Saber, and ebrary Inc, eds. Discrete dynamics and difference equations: Proceedings of the twelfth International Conference on Difference Equations and Applications, Lisbon, Portugal, 23 - 27 July 2007. Singapore: World Scientific Pub. Co., 2010.

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21

Strikwerda, J. C. Regularity estimates up to the boundary for elliptic systems of difference equations. Hampton, Va: ICASE, 1986.

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22

M, Johnson R. Linear differential and difference equations: A systems approach for mathematicians and engineers. Chichester: Albion Pub., 1997.

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23

service), ScienceDirect (Online, ed. Discrete dynamical systems, bifurcations and chaos in economics. Amsterdam: Elsevier, 2006.

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24

Kocic, V. L. Global Behavior of Nonlinear Difference Equations of Higher Order with Applications. Dordrecht: Springer Netherlands, 1993.

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25

Reyn, John. Phase portraits of planar quadratic systems. New York: Springer, 2011.

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26

Howind, Jochen. Analyse des stochastischen Modells von GPS-Trägerphasenbeobachtungen / von Jochen Howind. München: Verlag der Bayerischen Akademie der Wissenschaften in Kommission beim Verlags C.H. Beck, 2005.

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27

Krause, Ulrich. Differenzengleichungen und Diskrete dynamische Systeme: Eine Einführung in Theorie und Anwendungen. Berlin: De Gruyter, 2012.

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28

Differential and difference equations through computer experiments: With supplementary diskettes containing PHASER : an animator/simulator for dynamical systems for IBM personal computers. 2nd ed. New York: Springer-Verlag, 1989.

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29

Saker, Samir. Oscillation theory of dynamic equations on time scales: Second and third orders. Saarbrücken, Germany: LAP Lambert Academic Publishing, 2010.

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30

Arendt, Wolfgang. Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations: 21st International Workshop on Operator Theory and Applications, Berlin, July 2010. Basel: Springer Basel, 2012.

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31

Jet Propulsion Laboratory (U.S.), ed. A fully redundant double difference algorithm for obtaining minimum variance estimates from GPS observations. Pasadena, Calif: National Aeronautics and Space Administration, Jet Propulsion Laboratory, California Institute of Technology, 1986.

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32

Capietto, Anna. Stability and Bifurcation Theory for Non-Autonomous Differential Equations: Cetraro, Italy 2011, Editors: Russell Johnson, Maria Patrizia Pera. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013.

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33

Discrete chaos: With applications in science and engineering. 2nd ed. Boca Raton: Chapman & Hall/CRC, 2008.

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34

Discrete chaos. Boca Raton, Fla: Chapman & Hall/CRC, 2000.

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35

Elwood, David Michael. A system involving a nonlinear first order partial differential equation coupled with a nonlinear Volterra integral equation. 1987.

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36

Rajeev, S. G. Fluid Mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.001.0001.

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Starting with a review of vector fields and their integral curves, the book presents the basic equations of the subject: Euler and Navier–Stokes. Some solutions are studied next: ideal flows using conformal transformations, viscous flows such as Couette and Stokes flow around a sphere, shocks in the Burgers equation. Prandtl’s boundary layer theory and the Blasius solution are presented. Rayleigh–Taylor instability is studied in analogy with the inverted pendulum, with a digression on Kapitza’s stabilization. The possibility of transients in a linearly stable system with a non-normal operator is studied using an example by Trefethen et al. The integrable models (KdV, Hasimoto’s vortex soliton) and their hamiltonian formalism are studied. Delving into deeper mathematics, geodesics on Lie groups are studied: first using the Lie algebra and then using Milnor’s approach to the curvature of the Lie group. Arnold’s deep idea that Euler’s equations are the geodesic equations on the diffeomorphism group is then explained and its curvature calculated. The next three chapters are an introduction to numerical methods: spectral methods based on Chebychev functions for ODEs, their application by Orszag to solve the Orr–Sommerfeld equation, finite difference methods for elementary PDEs, the Magnus formula and its application to geometric integrators for ODEs. Two appendices give an introduction to dynamical systems: Arnold’s cat map, homoclinic points, Smale’s horse shoe, Hausdorff dimension of the invariant set, Aref ’s example of chaotic advection. The last appendix introduces renormalization: Ising model on a Cayley tree and Feigenbaum’s theory of period doubling.
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37

Ahlbrandt, Calvin. Discrete Hamiltonian Systems: "Difference Equations, Continued Fractions, And Riccati Equations". Springer, 2010.

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38

Peterson, A. C., and Calvin Ahlbrandt. Discrete Hamiltonian Systems: Difference Equations, Continued Fractions, and Riccati Equations. Springer, 2013.

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39

Peterson, Allan, and Martin Bohner. Dynamic Equations on Time Scales. Birkhäuser, 2012.

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40

Dean, Donald L. Discrete Field Analysis of Structural Systems. Springer London, Limited, 2014.

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41

Merino, Orlando, Mustafa R. S. Kulenovic, and Kulenovic M R S (Mustafa R S ). Discrete Dynamical Systems and Difference Equations with Mathematica. Taylor & Francis Group, 2002.

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42

Merino, Orlando, and Mustafa R. S. Kulenovic. Discrete Dynamical Systems and Difference Equations with Mathematica. Taylor & Francis Group, 2019.

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43

Merino, Orlando, and Mustafa R. S. Kulenovic. Discrete Dynamical Systems and Difference Equations with Mathematica. Taylor & Francis Group, 2002.

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44

Merino, Orlando, and Mustafa R. S. Kulenovic. Discrete Dynamical Systems and Difference Equations with Mathematica. Chapman & Hall/CRC, 2002.

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45

Merino, Orlando, and Mustafa R. S. Kulenovic. Discrete Dynamical Systems and Difference Equations with Mathematica. Taylor & Francis Group, 2002.

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46

Peterson, Allan C., and Martin Bohner. Advances in Dynamic Equations on Time Scales. Birkhauser Verlag, 2011.

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47

Advances in Dynamic Equations on Time Scales. Birkhauser, 2003.

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48

(Editor), Martin Bohner, and Allan C. Peterson (Editor), eds. Advances in Dynamic Equations on Time Scales. Birkhäuser Boston, 2002.

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49

Peterson, Allan C., and Martin Bohner. Advances in Dynamic Equations on Time Scales. Birkhäuser, 2012.

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50

Zhang, Xiang. Integrability of Dynamical Systems: Algebra and Analysis. Springer Singapore Pte. Limited, 2017.

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