The dielectric barrier discharge is recognized as one of the efficient methods of ultraviolet light generation and ozone production. As well, it is widely utilized for gaseous wastes neutralization and other technological processes in industry. This electrochemical reaction is electrically equivalent to a nonlinear capacitive load that represents some difficulties for designing the power supply. Therefore, a conventional power supply is designed for a drastically simplified model of the load and generally is not optimal. This paper presents a fast simulation approach for the nonlinear capacitive model representation of the dielectric barrier discharge load lamp. The main idea of the proposed method is to use analytical solutions of the differential state equations for the load and find the unknown initial conditions for the steady state by an optimization method. The derived expressions for the analytical solutions are rather complicated, however they greatly reduce the calculation time, which make sense when a deeper analysis is performed. This paper introduces the proposed simulation method and gives some examples of its application such as estimation of the load equivalent parameters and load matching conditions.