A Set of Python /Cython Wrappers for Extrapolation Based Solvers for Differential Algebraic System
(2014) In Master Thesis in Mathematical Science NUMM11 20131Mathematics (Faculty of Engineering)
- Abstract
- My thesis is a part of the Assimulo project which is a simulation package for solving ordinary differential equations. It is written in the high-level programming language Python and combines a variety of different solvers written in FORTRAN, C, and even Python via a common interface. In my thesis, extrapolation methods for initial value problems are studied in two parts: Ordinary Differential Equation systems (ODEs) and Differential- Algebraic Equations (DAEs). Much research has been done on this area by mathematicians such as Richardson, Romberg, Dahlquist, Bulirsch, and Gear, to improve both implicit and explicit methods for numerically solving ODEs.
In this work some discretizations, that are suited for combination with... (More) - My thesis is a part of the Assimulo project which is a simulation package for solving ordinary differential equations. It is written in the high-level programming language Python and combines a variety of different solvers written in FORTRAN, C, and even Python via a common interface. In my thesis, extrapolation methods for initial value problems are studied in two parts: Ordinary Differential Equation systems (ODEs) and Differential- Algebraic Equations (DAEs). Much research has been done on this area by mathematicians such as Richardson, Romberg, Dahlquist, Bulirsch, and Gear, to improve both implicit and explicit methods for numerically solving ODEs.
In this work some discretizations, that are suited for combination with extrapolation, are discussed and evaluated. Both non-stiff and stiff integration are covered and changed by using polynomial interpolation and stepsize control. In the DAE part of this thesis, the focus is on a FORTRAN code, by Lubich, Nowak, Pöhle, and Engstler which is an extrapolation integrator for mechanical systems.
There are many well written FORTRAN codes available, so I developed wrappers for these codes using F2Py to provide them in Assimulo. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/4823857
- author
- Abiri, Nadjmeh LU
- supervisor
-
- Claus Führer LU
- organization
- course
- NUMM11 20131
- year
- 2014
- type
- H2 - Master's Degree (Two Years)
- subject
- publication/series
- Master Thesis in Mathematical Science
- report number
- LUNFNA-3019-2014
- ISSN
- 1404-6342
- other publication id
- 2014:E56
- language
- English
- id
- 4823857
- date added to LUP
- 2014-12-15 11:49:20
- date last changed
- 2016-02-02 20:59:50
@misc{4823857, abstract = {{My thesis is a part of the Assimulo project which is a simulation package for solving ordinary differential equations. It is written in the high-level programming language Python and combines a variety of different solvers written in FORTRAN, C, and even Python via a common interface. In my thesis, extrapolation methods for initial value problems are studied in two parts: Ordinary Differential Equation systems (ODEs) and Differential- Algebraic Equations (DAEs). Much research has been done on this area by mathematicians such as Richardson, Romberg, Dahlquist, Bulirsch, and Gear, to improve both implicit and explicit methods for numerically solving ODEs. In this work some discretizations, that are suited for combination with extrapolation, are discussed and evaluated. Both non-stiff and stiff integration are covered and changed by using polynomial interpolation and stepsize control. In the DAE part of this thesis, the focus is on a FORTRAN code, by Lubich, Nowak, Pöhle, and Engstler which is an extrapolation integrator for mechanical systems. There are many well written FORTRAN codes available, so I developed wrappers for these codes using F2Py to provide them in Assimulo.}}, author = {{Abiri, Nadjmeh}}, issn = {{1404-6342}}, language = {{eng}}, note = {{Student Paper}}, series = {{Master Thesis in Mathematical Science}}, title = {{A Set of Python /Cython Wrappers for Extrapolation Based Solvers for Differential Algebraic System}}, year = {{2014}}, }