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Semi-Implicit Trapezoidal Rule

The semi-implicit trapezoidal rule method is given by [556]

$\displaystyle \underline{\hat{x}}(n) \isdefs \underline{\hat{x}}(n-1) + \frac{T}{2}\, \frac{f[n,\underline{\hat{x}}(n-1),\underline{u}(n)] + f[n-1,\underline{\hat{x}}(n-1),\underline{u}(n)]}{1-\frac{T}{2}\,\ddot{\underline{\hat{x}}}(n-1)}. \protect$ (8.16)


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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4.
Copyright © 2015-05-22 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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