Minimization of the error in the calculation of the steady state by shooting methods

The periodic steady state of a circuit can be calculated with a variety of algorithms. One of them is the (multiple-) shooting method. For good performance, the shooting analysis uses a higher order multistep backward-integration method for the computation. Normally, in the very first step, the Gear 1 integration formula is used because no information of previous discretization points are available. The next step can be calculated with the second-order formula. After the calculation of (k-1) successive time-steps, it is possible to switch to the desired (kth-order) integration formula. The switching introduces an error to the solution of the steady state, which can be observed by a subsequent Fourier transformation. This paper presents a straightforward method to suppress the problem by generating additional starting values. The novel formulation is compared with the conventional shooting method on two example circuits.