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Improving the accuracy of BDF methods for index 3 dierential algebraic equations

Arévalo, Carmen LU and Lötstedt, Per (1995) In BIT 35(3). p.297-308
Abstract
Methods for solving index 3 DAEs based on BDFs suffer a loss of accuracy when there is a change of step size or a change of order of the method. A layer of nonuniform convergence is observed in these cases, and O(1) errors may appear in the algebraic variables. From the viewpoint of error control, it is beneficial to allow smooth changes of step size, and since most codes based on BDFs are of variable order, it is also of interest to avoid the inaccuracies caused by a change of order of the method. In the case of BDFs applied to index 3 DAEs in semi-explicit form, we present algorithms that correct to O(h) the inaccurate approximations to the algebraic variables when there are changes of step size in the backward Euler method. These... (More)
Methods for solving index 3 DAEs based on BDFs suffer a loss of accuracy when there is a change of step size or a change of order of the method. A layer of nonuniform convergence is observed in these cases, and O(1) errors may appear in the algebraic variables. From the viewpoint of error control, it is beneficial to allow smooth changes of step size, and since most codes based on BDFs are of variable order, it is also of interest to avoid the inaccuracies caused by a change of order of the method. In the case of BDFs applied to index 3 DAEs in semi-explicit form, we present algorithms that correct to O(h) the inaccurate approximations to the algebraic variables when there are changes of step size in the backward Euler method. These algorithms can be included in an existing code at a very small cost. We have also described how to obtain formulas that correct the O(1) errors in the algebraic variables appearing after a change of order. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
BDF, differential-algebraic equation, index 3
in
BIT
volume
35
issue
3
pages
12 pages
publisher
Springer
external identifiers
  • scopus:34249757482
ISSN
0006-3835
DOI
10.1007/BF01732606
language
English
LU publication?
yes
id
fc769ff3-7e16-439c-bb6c-f1b2e13d45bf
date added to LUP
2017-02-08 09:44:36
date last changed
2017-05-14 04:47:55
@article{fc769ff3-7e16-439c-bb6c-f1b2e13d45bf,
  abstract     = {Methods for solving index 3 DAEs based on BDFs suffer a loss of accuracy when there is a change of step size or a change of order of the method. A layer of nonuniform convergence is observed in these cases, and O(1) errors may appear in the algebraic variables. From the viewpoint of error control, it is beneficial to allow smooth changes of step size, and since most codes based on BDFs are of variable order, it is also of interest to avoid the inaccuracies caused by a change of order of the method. In the case of BDFs applied to index 3 DAEs in semi-explicit form, we present algorithms that correct to O(h) the inaccurate approximations to the algebraic variables when there are changes of step size in the backward Euler method. These algorithms can be included in an existing code at a very small cost. We have also described how to obtain formulas that correct the O(1) errors in the algebraic variables appearing after a change of order.},
  author       = {Arévalo, Carmen and Lötstedt, Per},
  issn         = {0006-3835},
  keyword      = {BDF,differential-algebraic equation,index 3},
  language     = {eng},
  number       = {3},
  pages        = {297--308},
  publisher    = {Springer},
  series       = {BIT},
  title        = {Improving the accuracy of BDF methods for index 3 dierential algebraic equations},
  url          = {http://dx.doi.org/10.1007/BF01732606},
  volume       = {35},
  year         = {1995},
}