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A Python implementation of modern Adaptive Multistep methods in the object oriented simulation tool Assimulo

Asim, Sadia LU (2020) In Master's Theses in Mathematical Sciences NUMM11 20201
Mathematics (Faculty of Engineering)
Mathematics (Faculty of Sciences)
Centre for Mathematical Sciences
Abstract
Linear multi-step methods have been around for more than a century now. But they were with a fixed step-size, where a lot of hand calculations had to be made to find the coefficients of each method separately. It is only recently that variable step-size methodology was introduced and built into the solver. In this thesis, we are exploring this new methodology and at the same time, implementing one of it's methods in Object-Oriented Simulation Tools called Assimulo, so that the method is industrially available for solving real life problems.

We will first give an introduction of the linear multi-step methods. Then we will dive into the methodology itself. After this we will give an introduction of the simulation tool: Assimulo and how it... (More)
Linear multi-step methods have been around for more than a century now. But they were with a fixed step-size, where a lot of hand calculations had to be made to find the coefficients of each method separately. It is only recently that variable step-size methodology was introduced and built into the solver. In this thesis, we are exploring this new methodology and at the same time, implementing one of it's methods in Object-Oriented Simulation Tools called Assimulo, so that the method is industrially available for solving real life problems.

We will first give an introduction of the linear multi-step methods. Then we will dive into the methodology itself. After this we will give an introduction of the simulation tool: Assimulo and how it works. Then we will come to the main part of the thesis i.e implementing these ideas in Assimulo. We will describe each phase of the implementation process separately, along with an overview of the obstacles faced and how they were tackled. The last section, before conclusion, will then be the experiments, where we have tested the new method in Assimulo by comparing our solver's performance with a variable step-size and variable order solver called CVODE. Last, we have a conclusion where we have summarized our results. We have found that although more work needs to be done in Assimulo, this new solver gives us results close to the CVODE, which is a C++ based solver/package. (Less)
Please use this url to cite or link to this publication:
author
Asim, Sadia LU
supervisor
organization
course
NUMM11 20201
year
type
H2 - Master's Degree (Two Years)
subject
keywords
Python, Assimulo, Object Oriented, Programming, Simulation tool, Multistep
publication/series
Master's Theses in Mathematical Sciences
report number
LUNFNA-3033-2020
ISSN
1404-6342
other publication id
2020:E82
language
English
id
9032113
date added to LUP
2021-06-08 17:06:57
date last changed
2021-06-08 17:06:57
@misc{9032113,
  abstract     = {{Linear multi-step methods have been around for more than a century now. But they were with a fixed step-size, where a lot of hand calculations had to be made to find the coefficients of each method separately. It is only recently that variable step-size methodology was introduced and built into the solver. In this thesis, we are exploring this new methodology and at the same time, implementing one of it's methods in Object-Oriented Simulation Tools called Assimulo, so that the method is industrially available for solving real life problems.

We will first give an introduction of the linear multi-step methods. Then we will dive into the methodology itself. After this we will give an introduction of the simulation tool: Assimulo and how it works. Then we will come to the main part of the thesis i.e implementing these ideas in Assimulo. We will describe each phase of the implementation process separately, along with an overview of the obstacles faced and how they were tackled. The last section, before conclusion, will then be the experiments, where we have tested the new method in Assimulo by comparing our solver's performance with a variable step-size and variable order solver called CVODE. Last, we have a conclusion where we have summarized our results. We have found that although more work needs to be done in Assimulo, this new solver gives us results close to the CVODE, which is a C++ based solver/package.}},
  author       = {{Asim, Sadia}},
  issn         = {{1404-6342}},
  language     = {{eng}},
  note         = {{Student Paper}},
  series       = {{Master's Theses in Mathematical Sciences}},
  title        = {{A Python implementation of modern Adaptive Multistep methods in the object oriented simulation tool Assimulo}},
  year         = {{2020}},
}