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Linearization via a geometric mean approximation
- f(u')=bu'|u'| leads to a quadratic equation for u^{n+1}
- Instead of solving the quadratic equation, we use a geometric mean
approximation
In general, the geometric mean approximation reads
(w^2)^n \approx w^{n-\half}w^{n+\half}\tp
For |u'|u' at t_n :
[u'|u'|]^n \approx u'(t_n+{\half})|u'(t_n-{\half})|\tp
For u' at t_{n\pm 1/2} we use centered difference:
u'(t_{n+1/2})\approx [D_t u]^{n+\half},\quad u'(t_{n-1/2})\approx [D_t u]^{n-\half}
