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Contents
Contents
Stability and Bifurcation
Linear Stability
Systems of ODEs with constant coefficients
Eigenvalues and eigenvectors
The exponential matrix
The adjoint problem
Variation of parameters
Phase plane
Stability and instability
Partial differential equations
Semigroups of operators
Linearization
The implicit function theorem
Nonlinear stability
The stable manifold theorem
Bifurcations
The center manifold theorem
Bifurcation at a simple eigenvalue
Hopf bifurcation
Bifurcation with symmetry
References
Examples in Viscoelasticity
Governing Equations
Parallel-Plate Flow
Problem formulation
Stability of torsional flow
Bifurcations
Appendix 1: Governing equations
Cone-and-Plate Flow
Base flow and its stability
Linear Stability
Hopf bifurcation
Appendix 1: Governing equations
Appendix 2: Linearized equations
Extensional Flow
Problem formulation
Ideal uniaxial elongation
Linear stability
Appendix 1: One-dimensional model
Appendix 2: Linearized equations
References
Numerical Methods for Viscoelastic Flow Simulations with Emphasis on Stability Analysis
Fundamentals on Numerical Methods
Fundamentals of FORTRAN 90 (95)
Linear algebraic problems
Direct Solution of
Iterative Approaches
Nonlinear algebraic problems
Newton's Method
Eigenvalue problems
QR Method
Arnoldi Method
Ordinary differential equations
Linear Multistep Methods
Runge-Kutta Methods
Appendix A
References
About this document ...
Michael Renardy
1998-07-13
