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A posteriori error estimates for leap-frog and cosine methods for second order evolution problems

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posted on 2023-06-09, 00:18 authored by Emmanuil H Georgoulis, Omar LakkisOmar Lakkis, Charalambos G Makridakis, Charalambos MakridakisCharalambos Makridakis
We consider second order explicit and implicit two-step time-discrete schemes for wave-type equations. We derive optimal order aposteriori estimates controlling the time discretization error. Our analysis, has been motivated by the need to provide aposteriori estimates for the popular leap-frog method (also known as Verlet's method in molecular dynamics literature); it is extended, however, to general cosine-type second order methods. The estimators are based on a novel reconstruction of the time-dependent component of the approximation. Numerical experiments confirm similarity of convergence rates of the proposed estimators and of the theoretical convergence rate of the true error.

History

Publication status

  • Published

File Version

  • Published version

Journal

SIAM Journal on Numerical Analysis (SINUM)

ISSN

0036-1429

Publisher

Society for Industrial and Applied Mathematics

Issue

1

Volume

54

Page range

120-136

Place of publication

Technical University Athens (GR), University of Sussex (GB), University of Leicester (GB)

Department affiliated with

  • Mathematics Publications

Notes

arXiv: 1411.7572

Institution

arXiv

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2016-02-16

First Open Access (FOA) Date

2016-11-03

First Compliant Deposit (FCD) Date

2016-02-16

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