Pseudospectra and the numerical solution of differential equations
(2021) In Master's Theses in Mathematical Sciences NUMM03 20211Mathematics (Faculty of Engineering)
Mathematics (Faculty of Sciences)
Centre for Mathematical Sciences
- Abstract
- Eigenvalue analysis has been a key tool to science and engineering for several
decades. Eigenvalues can predict the behaviour of many mathematical systems
of equations but alone they cannot fully explain phenomena such as stability
or stiffness. Together, eigenvalues and pseudospectra can give a better understanding
of several phenomena such as instability in nonnormal matrices or
operators.
In this thesis, the basic concepts of pseudospectra are utilized to assist in understanding
how pseudospectra can better explain the stability of PDE discretizations,
the stability of the method of lines, the stiffness of ODEs and the
GKS-stability of boundary conditions.
It has been based on the book of Lloyd N. Trefethen and Mark Embree,... (More) - Eigenvalue analysis has been a key tool to science and engineering for several
decades. Eigenvalues can predict the behaviour of many mathematical systems
of equations but alone they cannot fully explain phenomena such as stability
or stiffness. Together, eigenvalues and pseudospectra can give a better understanding
of several phenomena such as instability in nonnormal matrices or
operators.
In this thesis, the basic concepts of pseudospectra are utilized to assist in understanding
how pseudospectra can better explain the stability of PDE discretizations,
the stability of the method of lines, the stiffness of ODEs and the
GKS-stability of boundary conditions.
It has been based on the book of Lloyd N. Trefethen and Mark Embree, "Spectra
and Pseudospectra The Behavior of Nonnormal Matrices and Operators"
[Trefethen and Embree, 2005]. Despite that, it tries to explain in a more analytical
manner certain points of the book. Using also other references, we
attempt to clarify some more aspects of pseudospectra. The code for the figures
has been based on Lloyd N. Trefethen [Trefethen, 1999] and is presented in the
Appendix. For more on MATLAB codes for solving problems using spectra and
pseudospectra, see [Trefethen, 2000].
i (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/9078457
- author
- Ioannidis, Mavroudis LU
- supervisor
-
- Claus Führer LU
- organization
- course
- NUMM03 20211
- year
- 2021
- type
- H2 - Master's Degree (Two Years)
- subject
- keywords
- Pseudospectra, numerical solutions of differential equations, spectral differentiation matrices, Lax-stability, stability of MOL, stiffness, GKSstability
- publication/series
- Master's Theses in Mathematical Sciences
- report number
- LUNFNA-3039-2022
- ISSN
- 1404-6342
- other publication id
- 2022:E83
- language
- English
- id
- 9078457
- date added to LUP
- 2024-05-13 16:36:25
- date last changed
- 2024-05-13 16:36:25
@misc{9078457, abstract = {{Eigenvalue analysis has been a key tool to science and engineering for several decades. Eigenvalues can predict the behaviour of many mathematical systems of equations but alone they cannot fully explain phenomena such as stability or stiffness. Together, eigenvalues and pseudospectra can give a better understanding of several phenomena such as instability in nonnormal matrices or operators. In this thesis, the basic concepts of pseudospectra are utilized to assist in understanding how pseudospectra can better explain the stability of PDE discretizations, the stability of the method of lines, the stiffness of ODEs and the GKS-stability of boundary conditions. It has been based on the book of Lloyd N. Trefethen and Mark Embree, "Spectra and Pseudospectra The Behavior of Nonnormal Matrices and Operators" [Trefethen and Embree, 2005]. Despite that, it tries to explain in a more analytical manner certain points of the book. Using also other references, we attempt to clarify some more aspects of pseudospectra. The code for the figures has been based on Lloyd N. Trefethen [Trefethen, 1999] and is presented in the Appendix. For more on MATLAB codes for solving problems using spectra and pseudospectra, see [Trefethen, 2000]. i}}, author = {{Ioannidis, Mavroudis}}, issn = {{1404-6342}}, language = {{eng}}, note = {{Student Paper}}, series = {{Master's Theses in Mathematical Sciences}}, title = {{Pseudospectra and the numerical solution of differential equations}}, year = {{2021}}, }