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Semi-Implicit Backward Euler

The semi-implicit backward Euler method is defined by [556]

$\displaystyle \underline{\hat{x}}(n) \isdefs \underline{\hat{x}}(n-1) + T\, \frac{f[n,\underline{\hat{x}}(n-1)]}{1-T\,\ddot{\underline{\hat{x}}}(n-1)} \protect$ (8.15)

where $ \ddot{\underline{\hat{x}}}(n-1)$ denotes an estimate of the second time derivative $ \ddot{\underline{x}}(t)$ .


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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4.
Copyright © 2014-03-23 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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