transient simulation of circuits with widely separated time constants and fast periodic excitations is not efficient because a long simulation period with small time steps is required. one approach to simulate the transient behaviour more efficiently is known as the multi partial differential equation (mpde). in the mpde the system ordinary differential equations that describe a circuit is transformed into a system of partial differential equations with two time variables, one for the fast periodic variations and another for the slow transient evolution. this method has been implemented in a general-purpose circuit simulator program named carrot. this thesis presents progress towards the development that simulator. the main contributions of this thesis are the implementation and validation of mosfet models in the simulator and the study of the performance of the mpde approach (as currently implemented in carrot) applied to complex cmos circuits. an overview of concepts relevant for this work is presented, followed by a detailed description of the mosfet model implementation. next, the design of an integrated cmos ring voltage-controlled oscillator is presented. this is followed by simulation case studies. the simulation results indicate that the mpde approach can achieve orders of magnitude of improvement in simulation speed compared to regular transient analysis. this thesis concludes with recommendations for future research.