Abstract
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.
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Penski, C. A numerical scheme for highly oscillatory DAEs and its application to circuit simulation. Numerical Algorithms 19, 173–181 (1998). https://doi.org/10.1023/A:1019194104440
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DOI: https://doi.org/10.1023/A:1019194104440