A linear prediction step can be used to obtain an initial-guess from
the previous solution. The two-level Newton scheme with a linear prediction
step is referred to as the modified two-level Newton algorithm. A first-order
prediction is made by use of the forward-Euler scheme,

x^{k + 1} = x^{k} +
^{ . }V

(4.12)

where V is the change in voltage from circuit iteration k to k + 1,
and
x/V is calculated as in (4.8). In the
investigations of [39] this algorithm had the most reliable
convergence properties.