A new numerical method for SDEs and its application in circuit simulation

In the context of computer-aided design of electric circuits, the modeling of circuits under the influence of electronic noise leads to stochastic differential-algebraic equations (SDAEs). A new numerical integration scheme for the pathwise approximative solution of stochastic differential equations (SDEs) is presented. The available numerical schemes for SDEs cannot solve these equations efficiently. The new discretization scheme is constructed by the means of Itô–Taylor expansions. A Fortran77 implementation of the presented integration scheme reduces the simulation time for a ring oscillator to about 85% compared with common methods.