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THIRD-ORDER TIME-STEP INTEGRATION METHODS WITH CONTROLLABLE NUMERICAL DISSIPATION

✍ Scribed by FUNG, T. C.

Publisher: John Wiley and Sons
Year: 1997
Tongue: English
Weight: 159 KB
Volume: 13
Category: Article
ISSN: 1069-8299
DOI: 10.1002/(sici)1099-0887(199704)13:4<307::aid-cnm64>3.0.co;2-2

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✦ Synopsis

In this paper, the second-order-accurate non-dissipative Newmark method is modi®ed to third-orderaccurate with controllable dissipation by using complex time steps. Among these algorithms, the asymptotic annihilating algorithm and the non-dissipative algorithm are found to be the ®rst sub-diagonal (1,2) and diagonal (2,2) PadeÂ approximations, respectively. The non-dissipative algorithm is therefore fourth-orderaccurate. The stability properties and errors for algorithms with other dissipations are between these two algorithms. The spectral radii, the algorithmic damping ratios and the relative period errors for the present third-order complex-time-step algorithms are compared favourably with other algorithms. # 1997 by

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