Details
| Original language | English |
|---|---|
| Pages (from-to) | 565-595 |
| Number of pages | 31 |
| Journal | International Journal for Numerical Methods in Engineering |
| Volume | 80 |
| Issue number | 5 |
| Publication status | Published - 1 Sept 2009 |
Abstract
The results produced by Richardson extrapolation, though, in general, very accurate, are inexact. Numerical evaluation of this inexactness and implementation of the evaluation in practice are the objectives of this paper. First, considering linear changes of errors in the convergence plots, asymptotic upper bounds are proposed for the errors. Then, the achievement is extended to the results produced by Richardson extrapolation, and finally, an error-controlling procedure is proposed and successfully implemented in approximate computations originated in science and engineering.
Keywords
- Convergence plot, Error upper-bound estimation, Practical implementation, Pseudo-convergence, Richardson extrapolation, Time integration analysis
ASJC Scopus subject areas
- Mathematics(all)
- Numerical Analysis
- Engineering(all)
- Mathematics(all)
- Applied Mathematics
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In: International Journal for Numerical Methods in Engineering, Vol. 80, No. 5, 01.09.2009, p. 565-595.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Asymptotic upper bounds for the errors of Richardson extrapolation with practical application in approximate computations
AU - Soroushian, Aram
AU - Wriggers, Peter
AU - Farjoodi, Jamshid
PY - 2009/9/1
Y1 - 2009/9/1
N2 - The results produced by Richardson extrapolation, though, in general, very accurate, are inexact. Numerical evaluation of this inexactness and implementation of the evaluation in practice are the objectives of this paper. First, considering linear changes of errors in the convergence plots, asymptotic upper bounds are proposed for the errors. Then, the achievement is extended to the results produced by Richardson extrapolation, and finally, an error-controlling procedure is proposed and successfully implemented in approximate computations originated in science and engineering.
AB - The results produced by Richardson extrapolation, though, in general, very accurate, are inexact. Numerical evaluation of this inexactness and implementation of the evaluation in practice are the objectives of this paper. First, considering linear changes of errors in the convergence plots, asymptotic upper bounds are proposed for the errors. Then, the achievement is extended to the results produced by Richardson extrapolation, and finally, an error-controlling procedure is proposed and successfully implemented in approximate computations originated in science and engineering.
KW - Convergence plot
KW - Error upper-bound estimation
KW - Practical implementation
KW - Pseudo-convergence
KW - Richardson extrapolation
KW - Time integration analysis
UR - http://www.scopus.com/inward/record.url?scp=70349904257&partnerID=8YFLogxK
U2 - 10.1002/nme.2642
DO - 10.1002/nme.2642
M3 - Article
AN - SCOPUS:70349904257
VL - 80
SP - 565
EP - 595
JO - International Journal for Numerical Methods in Engineering
JF - International Journal for Numerical Methods in Engineering
SN - 0029-5981
IS - 5
ER -