NUMERICAL INTEGRATION OF DIFFERENTIAL EQUATIONS - Computer Methods for Analysis of Mixed-Mode Switching Circuits - page 57

Because and are constant for the derivative

of (4.13) with respect to gives

Newton-Raphson iterations proceed as follows

and

Integration stops when is sufficiently small.

3. Integration Using Numerical Laplace Inversion
LMS-PC algorithms improve the accuracy by employing more past
data. Its accuracy, however, is still limited because only the first-order
derivatives of the past data points are used. For linear circuits, the accu-
racy of numerical integration can be significantly improved by consider-
ing high-order derivatives. This section introduces a numerical Laplace
inversion based high-order numerical integration method for linear cir-
cuits.