Richardson Extrapolation combined with the sequential splitting procedure and the θ-method

Zahari Zlatev; István Faragó; Ágnes Havasi

Open Mathematics (2012)

  • Volume: 10, Issue: 1, page 159-172
  • ISSN: 2391-5455

Abstract

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Initial value problems for systems of ordinary differential equations (ODEs) are solved numerically by using a combination of (a) the θ-method, (b) the sequential splitting procedure and (c) Richardson Extrapolation. Stability results for the combined numerical method are proved. It is shown, by using numerical experiments, that if the combined numerical method is stable, then it behaves as a second-order method.

How to cite

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Zahari Zlatev, István Faragó, and Ágnes Havasi. "Richardson Extrapolation combined with the sequential splitting procedure and the θ-method." Open Mathematics 10.1 (2012): 159-172. <http://eudml.org/doc/269343>.

@article{ZahariZlatev2012,
abstract = {Initial value problems for systems of ordinary differential equations (ODEs) are solved numerically by using a combination of (a) the θ-method, (b) the sequential splitting procedure and (c) Richardson Extrapolation. Stability results for the combined numerical method are proved. It is shown, by using numerical experiments, that if the combined numerical method is stable, then it behaves as a second-order method.},
author = {Zahari Zlatev, István Faragó, Ágnes Havasi},
journal = {Open Mathematics},
keywords = {Initial value problems; Ordinary differential equations; Sequential splitting; Richardson Extrapolation; Stability; Cauchy problem; weighted scheme of quadrature formulas; Richardson extrapolation rule; system; stability},
language = {eng},
number = {1},
pages = {159-172},
title = {Richardson Extrapolation combined with the sequential splitting procedure and the θ-method},
url = {http://eudml.org/doc/269343},
volume = {10},
year = {2012},
}

TY - JOUR
AU - Zahari Zlatev
AU - István Faragó
AU - Ágnes Havasi
TI - Richardson Extrapolation combined with the sequential splitting procedure and the θ-method
JO - Open Mathematics
PY - 2012
VL - 10
IS - 1
SP - 159
EP - 172
AB - Initial value problems for systems of ordinary differential equations (ODEs) are solved numerically by using a combination of (a) the θ-method, (b) the sequential splitting procedure and (c) Richardson Extrapolation. Stability results for the combined numerical method are proved. It is shown, by using numerical experiments, that if the combined numerical method is stable, then it behaves as a second-order method.
LA - eng
KW - Initial value problems; Ordinary differential equations; Sequential splitting; Richardson Extrapolation; Stability; Cauchy problem; weighted scheme of quadrature formulas; Richardson extrapolation rule; system; stability
UR - http://eudml.org/doc/269343
ER -

References

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