This paper presents a new simulation method for fast evaluation of non-linear circuits. The proposed approach solves the non-linear ordinary differential equation set of the system using a semi-analytical solution based on the matrix exponential. In this paper, an analog signal processing front-end for discrete-time data acquisition system is considered as case study. The model includes non-linearity associated to switches, capacitive parasitics, finite non-linear DC-gain and non-linear settling behavior including slew-rate. Comparison with traditional ODE numerical solvers shows a reduction of the computation time in more than two orders of magnitude with negligible difference in terms of accuracy.