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Books on the topic 'Stability and asymptotics of difference equations'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Yee, H. C. Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. National Aeronautics and Space Administration, 1990.

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2

Yee, H. C. Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. National Aeronautics and Space Administration, 1990.

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3

1956-, Dos̆lá Zuzana, and Graef John R. 1942-, eds. The nonlinear limit-point/limit-circle problem. Birkhäuser, 2003.

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4

Difference equations in normed spaces: Stability and oscillations. Elsevier, 2007.

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5

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

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6

Shaĭkhet, L. E. Lyapunov functionals and stability of stochastic difference equations. Springer, 2011.

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7

P, Matus P., and Vabishchevich P. N, eds. Difference schemes with operator factors. Kluwer Academic, 2002.

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8

Jeltsch, Rolf. Barriers to the accuracy of explicit three-time-level difference schemes for hyperbolic equations. Universiteit van Stellenbosch, 1992.

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9

Shaikhet, Leonid. Lyapunov Functionals and Stability of Stochastic Functional Differential Equations. Springer International Publishing, 2013.

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10

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

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11

Orlik, Lyubov', and Galina Zhukova. Operator equation and related questions of stability of differential equations. 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 existe

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12

Warming, Robert F. An eigenvalue analysis of finite-difference approximations for hyperbolic IBVPs. National Aeronautics and Space Administration, Ames Research Center, 1989.

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13

Herrmann, Samuel. Stochastic resonance: A mathematical approach in the small noise limit. American Mathematical Society, 2014.

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14

Asymptotic Methods in Resonance Analytical Dynamics: Stability and Control: Theory, Methods and Applications; Volume 21. CRC, 2004.

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15

Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. National Aeronautics and Space Administration, 1995.

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16

Mathematics of Continuous and Discrete Dynamical Systems (Contemporary Mathematics). Amer Mathematical Society, 2012.

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17

Bartusek, Miroslav, Zuzana Doslá, and John R. Graef. The Nonlinear Limit-Point/Limit-Circle Problem. Birkhäuser Boston, 2003.

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18

Shaikhet, Leonid. Lyapunov Functionals and Stability of Stochastic Difference Equations. Springer, 2011.

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19

Difference equations in normed spaces - Stability and oscillations. Elsevier, 2007. http://dx.doi.org/10.1016/s0304-0208(07)x8002-2.

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20

Michael, Rassias John, ed. Functional equations, difference inequalities, and Ulam stability notions (F.U.N.). Nova Science Publishers, 2009.

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21

Gil, Michael. Difference Equations in Normed Spaces, Volume 206: Stability and Oscillations (North-Holland Mathematics Studies) (North-Holland Mathematics Studies). Elsevier Science, 2007.

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22

Shaikhet, Leonid. Lyapunov Functionals and Stability of Stochastic Functional Differential Equations. Springer, 2013.

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23

Shaikhet, Leonid. Lyapunov Functionals and Stability of Stochastic Functional Differential Equations. Springer, 2015.

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24

Jan, Nordstrom, Gottlieb David, and Institute for Computer Applications in Science and Engineering., eds. A stable and conservative interface treatment of arbitrary spatial accuracy. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1998.

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25

An eigenvalue analysis of finite-difference approximations for hyperbolic IBVPs. National Aeronautics and Space Administration, Ames Research Center, 1989.

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26

Boudreau, Joseph F., and Eric S. Swanson. Continuum dynamics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198708636.003.0019.

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The theory and application of a variety of methods to solve partial differential equations are introduced in this chapter. These methods rely on representing continuous quantities with discrete approximations. The resulting finite difference equations are solved using algorithms that stress different traits, such as stability or accuracy. The Crank-Nicolson method is described and extended to multidimensional partial differential equations via the technique of operator splitting. An application to the time-dependent Schrödinger equation, via scattering from a barrier, follows. Methods for solv

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