In this paper, new numerical integration algorithms with artificial damping effect are proposed which can be applied to the constant, pure PTA method to find DC operating points of nonlinear circuits when the Newton-Raphson method fails. This method can effectively avoid the oscillation and the “time step too small” problems compared with conventional PTA algorithms. The mathematical description for this method is presented. The application of the proposed method is illustrated by solving practical CMOS nonlinear circuits.