Implementation of 3 stage Lobatto IIIC into the Assimulo package
(2021) In Bachelor's Theses in Mathematical Sciences NUMK11 20211Mathematics (Faculty of Sciences)
Centre for Mathematical Sciences
- Abstract
- In recent years, the popularity of discontinuous Galerkin methods has increased. As shown in [19], a result exists that states that the Discontinuous Galerkin space approximations (DG) are equivalent to the Lobatto IIIC Runge-Kutta method. This thesis therefore outlines the adaptation of Hairer’s implementation of the Radau IIA Runge-Kutta method to the Lobatto IIIC method, extended with an adaptation of Pinto et al.’s two step error estimation found in [17]. As an alternative to the classical Three staged Radau IIA Runge Kutta method.
- Popular Abstract
- Ordinary differential equations (ODEs) are the backbone of physics, chemistry and biology. However these cannot be solved over a continuous region in time and space, rather they need to be solved on a discrete grid, while iterating over different points in time.
Runge Kutta methods are one of the methods to solve these problems. In this thesis we discuss the implementation of one such method, the Lobatto IIIC, by adapting the implementation of a similar method, the Radau IIA, done by Hairer [14]. Further we expand upon the implementation by including a newer method by pinto et al. for the local error estimation at the different steps [17].
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/9068401
- author
- Lehsten, Edmund Aristid LU
- supervisor
- organization
- alternative title
- Implementering av 3 stage Lobatto IIIC i Assimulo paketet
- course
- NUMK11 20211
- year
- 2021
- type
- M2 - Bachelor Degree
- subject
- keywords
- 3 Stage Lobatto IIIC, Lobatto IIIC, Assimulo
- publication/series
- Bachelor's Theses in Mathematical Sciences
- report number
- LUNFNA-4039-2021
- ISSN
- 1654-6229
- other publication id
- 2021:K45
- language
- English
- id
- 9068401
- date added to LUP
- 2022-01-19 15:13:28
- date last changed
- 2022-01-19 15:13:28
@misc{9068401, abstract = {{In recent years, the popularity of discontinuous Galerkin methods has increased. As shown in [19], a result exists that states that the Discontinuous Galerkin space approximations (DG) are equivalent to the Lobatto IIIC Runge-Kutta method. This thesis therefore outlines the adaptation of Hairer’s implementation of the Radau IIA Runge-Kutta method to the Lobatto IIIC method, extended with an adaptation of Pinto et al.’s two step error estimation found in [17]. As an alternative to the classical Three staged Radau IIA Runge Kutta method.}}, author = {{Lehsten, Edmund Aristid}}, issn = {{1654-6229}}, language = {{eng}}, note = {{Student Paper}}, series = {{Bachelor's Theses in Mathematical Sciences}}, title = {{Implementation of 3 stage Lobatto IIIC into the Assimulo package}}, year = {{2021}}, }