4.1.2 Modified Two-Level Newton Algorithm

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,

$$\left.\vphantom{ \frac{\partial \mathbf{x}}{\partial V} }\right. {\frac{\partial \mathbf{x}}{\partial V}} \left.\vphantom{ \frac{\partial \mathbf{x}}{\partial V} }\right\vert _{k}^{} \Delta$$ (4.12)

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