Technical Reports

The ICICS/CS Reading Room

UBC CS TR-88-12 Summary

On Symmetric Schemes and Differential-Algebraic Equations., June 1988 Uri Ascher

An example is given which demonstrates a potential risk in using symmetric difference schemes for initial value differential-algebraic equations (DAEs) or for very stiff ODEs. The basic difficulty is that the stability of the scheme is controlled by the stability of an auxiliary (ghost) ODE problem which is not necessarily stable even when the given problem is. \n The stability of symmetric schemes is better understood in the context of boundary value problems. In this context, such schemes are more naturally applied as well. For initial value problems, better alternatives may exist. A computational algorithm is proposed for boundary value index-l DAEs.

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