Contrary to many other applications of numerical system simulation, integrated circuit problems don't lend themselves to a formulation of state-space models, since the space charge in a p-n junction is a nonlinear and noninvertible function of the voltage across the junction. Therefore, it is necessary to employ numnerical differentiation instead of numerical integration in this type of simulation study.
The numerical algorithms employed in today's circuit simulators are fairly primitive. SPICE, for example, offers only two very simple implementations of the trapezoidal rule and of the backwards differentiation formula.
This thesis describes the design and implementation of DBDF, a specification of the inverted Gear algorithm in its Nordsieck form. A formal stability and truncation error analysis are included.
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