Semi-Implicit Backward Euler

The semi-implicit backward Euler method is defined by [555]

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