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A new numerical integration scheme for the simulation of differential–algebraic equations is presented. In the context of
the computer-aided design of electronic circuits, the modeling of highly oscillatory circuits leads to oscillatory differential–algebraic
equations mostly of index 1 or 2. Standard schemes can solve these equations neither efficiently nor reliably. The new discretiziation
scheme is constructed in such a way as to overcome the problems of classical numerical methods. It uses the Principle of Coherence
due to Hersch in combination with a multistep approach. A combined Maple and Fortran77 implementation of the presented integration
scheme reduces the simulation time for a quartz-controlled oscillator to about 2% compared with standard methods. Therefore,
it is a powerful tool for the design of highly oscillatory circuits.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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