The Resource Attractors under discretisation, Xiaoying Han, Peter Kloeden, (electronic book)
Attractors under discretisation, Xiaoying Han, Peter Kloeden, (electronic book)
Resource Information
The item Attractors under discretisation, Xiaoying Han, Peter Kloeden, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.This item is available to borrow from 1 library branch.
Resource Information
The item Attractors under discretisation, Xiaoying Han, Peter Kloeden, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.
This item is available to borrow from 1 library branch.
- Extent
- 1 online resource.
- 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
- Isbn
- 9783319619330
- Label
- Attractors under discretisation
- Title
- Attractors under discretisation
- Statement of responsibility
- Xiaoying Han, Peter Kloeden
- Language
- eng
- 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)
- 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)
- 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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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.liverpool.ac.uk/portal/Attractors-under-discretisation-Xiaoying-Han/l5Og4CEV_uE/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.liverpool.ac.uk/portal/Attractors-under-discretisation-Xiaoying-Han/l5Og4CEV_uE/">Attractors under discretisation, Xiaoying Han, Peter Kloeden, (electronic book)</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.liverpool.ac.uk/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.liverpool.ac.uk/">University of Liverpool</a></span></span></span></span></div>
