Numerical solution of stochastic differential-algebraic equations with applications to transient noise simulation of microelectronic circuits

The transient simulation of noise in electronic circuits leads to differential-algebraic equations, additively disturbed by white noise. For these systems, we present a mathematical model based on the theory of stochastic differential equations, along with an implicit two-step method for their numerical treatment. This numerical scheme works directly on the given structure of the equations which makes very efficient implementations possible. The order of convergence is preserved. The theoretical results are verified by numerical noise simulations of benchmark circuits.