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Implementation of 3 stage Lobatto IIIC into the Assimulo package

Lehsten, Edmund Aristid LU (2021) In Bachelor's Theses in Mathematical Sciences NUMK11 20211
Mathematics (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].
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author
Lehsten, Edmund Aristid LU
supervisor
organization
alternative title
Implementering av 3 stage Lobatto IIIC i Assimulo paketet
course
NUMK11 20211
year
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}},
}