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The Resource Attractors under discretisation, Xiaoying Han, Peter Kloeden, (electronic book)

Attractors under discretisation, Xiaoying Han, Peter Kloeden, (electronic book)

Label
Attractors under discretisation
Title
Attractors under discretisation
Statement of responsibility
Xiaoying Han, Peter Kloeden
Creator
Contributor
Subject
Language
eng
Member of
Cataloging source
YDX
http://library.link/vocab/creatorName
Han, Xiaoying
Dewey number
  • 515/.39
  • 510
Index
no index present
LC call number
  • QA614.813
  • QA1-939
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
Kloeden, Peter E
Series statement
SpringerBriefs in mathematics
http://library.link/vocab/subjectName
Attractors (Mathematics)
Label
Attractors under discretisation, Xiaoying Han, Peter Kloeden, (electronic book)
Instantiates
Publication
Contents
  • Preface; Contents; About the Authors; Part I Dynamical Systems and Numerical Schemes; 1 Lyapunov Stability and Dynamical Systems; 1.1 Lyapunov Stability; 1.2 Autonomous Dynamical Systems; 1.3 Invariant Sets; 1.4 Limit Sets; 1.5 Attractors; 2 One Step Numerical Schemes; 2.1 Discretisation Error; 2.2 General One Step Schemes; 2.2.1 Taylor Schemes; 2.2.2 Schemes Derived by Integral Approximations; 2.3 Orders of Local and Global Convergence; 2.4 Consistency; 2.5 Numerical Instability; 2.6 Steady States of Numerical Schemes; Part II Steady States Under Discretisation; 3 Linear Systems
  • 3.1 Linear ODE in mathbbR13.2 Linear ODE in mathbbC1; 3.3 The General Linear Case; 4 Lyapunov Functions; 4.1 Linear Systems Revisited; 4.2 Application: The Linear Euler Scheme; 4.3 Application: The Nonlinear Euler Scheme; 5 Dissipative Systems with Steady States; 6 Saddle Points Under Discretisation; 6.1 Saddle Points and the Euler Scheme; 6.1.1 A Nonlinear Example; 6.1.2 Shadowing; 6.2 General Case: Beyn's Theorem; Part III Autonomous Attractors Under Discretisation; 7 Dissipative Systems with Attractors; 7.1 Euler Scheme Dynamics; 7.2 Convergence of the Numerical Attractors
  • 8 Lyapunov Functions for Attractors8.1 Lyapunov Stability of Sets; 8.2 Yoshizawa's Theorem; 9 Discretisation of an Attractor: General Case; Part IV Nonautonomous Limit Sets Under Discretisation; 10 Dissipative Nonautonomous Systems; 10.1 Nonautonomous Omega Limit Sets; 10.2 Asymptotic Invariance; 10.2.1 Asymptotic Positive Invariance; 10.2.2 Asymptotic Negative Invariance; 11 Discretisation of Nonautonomous Limit Sets ; 11.1 The Implicit Euler Scheme; 11.2 Upper Semi Continuous Converence of the Numerical Omega Limit Sets; 12 Variable Step Size Discretisation of Autonomous Attractors
  • 12.1 Variable Time Step Limit Sets12.2 Upper Semi Continuous Convergence of the Numerical Omega Limit Sets; 13 Discretisation of a Uniform Pullback Attractor; Notes; References
Dimensions
unknown
Extent
1 online resource.
Form of item
online
Isbn
9783319619330
Specific material designation
remote
Label
Attractors under discretisation, Xiaoying Han, Peter Kloeden, (electronic book)
Publication
Contents
  • Preface; Contents; About the Authors; Part I Dynamical Systems and Numerical Schemes; 1 Lyapunov Stability and Dynamical Systems; 1.1 Lyapunov Stability; 1.2 Autonomous Dynamical Systems; 1.3 Invariant Sets; 1.4 Limit Sets; 1.5 Attractors; 2 One Step Numerical Schemes; 2.1 Discretisation Error; 2.2 General One Step Schemes; 2.2.1 Taylor Schemes; 2.2.2 Schemes Derived by Integral Approximations; 2.3 Orders of Local and Global Convergence; 2.4 Consistency; 2.5 Numerical Instability; 2.6 Steady States of Numerical Schemes; Part II Steady States Under Discretisation; 3 Linear Systems
  • 3.1 Linear ODE in mathbbR13.2 Linear ODE in mathbbC1; 3.3 The General Linear Case; 4 Lyapunov Functions; 4.1 Linear Systems Revisited; 4.2 Application: The Linear Euler Scheme; 4.3 Application: The Nonlinear Euler Scheme; 5 Dissipative Systems with Steady States; 6 Saddle Points Under Discretisation; 6.1 Saddle Points and the Euler Scheme; 6.1.1 A Nonlinear Example; 6.1.2 Shadowing; 6.2 General Case: Beyn's Theorem; Part III Autonomous Attractors Under Discretisation; 7 Dissipative Systems with Attractors; 7.1 Euler Scheme Dynamics; 7.2 Convergence of the Numerical Attractors
  • 8 Lyapunov Functions for Attractors8.1 Lyapunov Stability of Sets; 8.2 Yoshizawa's Theorem; 9 Discretisation of an Attractor: General Case; Part IV Nonautonomous Limit Sets Under Discretisation; 10 Dissipative Nonautonomous Systems; 10.1 Nonautonomous Omega Limit Sets; 10.2 Asymptotic Invariance; 10.2.1 Asymptotic Positive Invariance; 10.2.2 Asymptotic Negative Invariance; 11 Discretisation of Nonautonomous Limit Sets ; 11.1 The Implicit Euler Scheme; 11.2 Upper Semi Continuous Converence of the Numerical Omega Limit Sets; 12 Variable Step Size Discretisation of Autonomous Attractors
  • 12.1 Variable Time Step Limit Sets12.2 Upper Semi Continuous Convergence of the Numerical Omega Limit Sets; 13 Discretisation of a Uniform Pullback Attractor; Notes; References
Dimensions
unknown
Extent
1 online resource.
Form of item
online
Isbn
9783319619330
Specific material designation
remote

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