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Runge-Kutta Starters for Multistep Methods to Simulate Systems with Discontinuities

Mohammadi, Fatemeh LU (2013) In Master's theses in mathematical sciences NUMM11 20131
Mathematics (Faculty of Engineering)
Abstract
The topic of the thesis is re-initialization of multistep methods for the solution of ordinary differential equations, in which there are frequent discontinuities in first or higher derivatives.
There are self-starting algorithms to start or restart a multistep method.
It is normally started by first using a one-step method and then increasing the order successively until the working order is reached, or by applying a Runge-Kutta method several times to obtain the adequate values for starting. These methods are quite expensive, so we are going to focus on a one step method which constructs the initial values for starting the multistep methods with fewer function evaluations than are used with a conventional Runge-Kutta method and that... (More)
The topic of the thesis is re-initialization of multistep methods for the solution of ordinary differential equations, in which there are frequent discontinuities in first or higher derivatives.
There are self-starting algorithms to start or restart a multistep method.
It is normally started by first using a one-step method and then increasing the order successively until the working order is reached, or by applying a Runge-Kutta method several times to obtain the adequate values for starting. These methods are quite expensive, so we are going to focus on a one step method which constructs the initial values for starting the multistep methods with fewer function evaluations than are used with a conventional Runge-Kutta method and that returns state values with high order accuracy.
We will see two different approaches, the first one obtains Nordsieck vectors and the second one derives the state values. The goal is to implement this starter in connection with LSODE and compare the results with its internal self-starting algorithm. (Less)
Please use this url to cite or link to this publication:
author
Mohammadi, Fatemeh LU
supervisor
organization
course
NUMM11 20131
year
type
H2 - Master's Degree (Two Years)
subject
keywords
Runge-Kutta, Multistep methods, Discontinuities, Nordsieck
publication/series
Master's theses in mathematical sciences
report number
LUNFMA-3016-2013
ISSN
1404-6342
other publication id
2013:E59
language
English
id
4196026
date added to LUP
2014-02-14 16:16:15
date last changed
2015-12-14 13:32:11
@misc{4196026,
  abstract     = {The topic of the thesis is re-initialization of multistep methods for the solution of ordinary differential equations, in which there are frequent discontinuities in first or higher derivatives.
There are self-starting algorithms to start or restart a multistep method.
It is normally started by first using a one-step method and then increasing the order successively until the working order is reached, or by applying a Runge-Kutta method several times to obtain the adequate values for starting. These methods are quite expensive, so we are going to focus on a one step method which constructs the initial values for starting the multistep methods with fewer function evaluations than are used with a conventional Runge-Kutta method and that returns state values with high order accuracy.
We will see two different approaches, the first one obtains Nordsieck vectors and the second one derives the state values. The goal is to implement this starter in connection with LSODE and compare the results with its internal self-starting algorithm.},
  author       = {Mohammadi, Fatemeh},
  issn         = {1404-6342},
  keyword      = {Runge-Kutta,Multistep methods,Discontinuities,Nordsieck},
  language     = {eng},
  note         = {Student Paper},
  series       = {Master's theses in mathematical sciences},
  title        = {Runge-Kutta Starters for Multistep Methods to Simulate Systems with Discontinuities},
  year         = {2013},
}