From: gdpusch@NO.xnet.SPAM.com (Gordon D. Pusch) Subject: Re: What algorithm uses DDASSL? Date: 25 Aug 2000 20:44:47 -0500 Newsgroups: sci.math.num-analysis Summary: [missing] bv writes: > Petr Kuzmic wrote: >> >> DIFFERENTIAL-ALGEBRAIC EQUATIONS ARE NOT ODES >> PETZOLD L > > A rather curious title considering that the author of DASSL purports to > solve, > > f(t,y,y') = 0 > > Does this look like an apple strudel to anyone? Anyhow, would someone > who read the article care to elaborate if the philosophical thrust of > the content justifies its (dubious?) title. The point the author is trying to make is that DAEs are not _ORDINARY_ differential equations, because for DAEs it's impossible to solve f(t,y,y') = 0 for the y' to yield a set of ODEs, y' = g(y,t), as many theorems in the theory of ODEs and most ODE solvers implicitly assume is possible. As a result, the behavior and solutions of DAEs are qualitatively different from those of ODEs. For details on the consequences of this, read the paper. -- Gordon D. Pusch perl -e '$_ = "gdpusch\@NO.xnet.SPAM.com\n"; s/NO\.//; s/SPAM\.//; print;' ============================================================================== From: Petr Kuzmic Subject: Re: What algorithm uses DDASSL? Date: Fri, 25 Aug 2000 23:51:48 -0500 Newsgroups: sci.math.num-analysis bv wrote: > > Petr Kuzmic wrote: > > > > DIFFERENTIAL-ALGEBRAIC EQUATIONS ARE NOT ODES > > PETZOLD L > > A rather curious title considering that the author of DASSL purports to > solve, > > f(t,y,y') = 0 > > Does this look like an apple strudel to anyone? Anyhow, would someone > who read the article care to elaborate if the philosophical thrust of > the content justifies its (dubious?) title. I don't know what "apple strudel" has to do with this topic, nor do I think that it is necessary to discuss a "philosophical thrust" of the article (which is available in better libraries for perusal by anyone surprised by its title). Rather, I believe that we might have a simple case of terminological confusion. Indeed, f(t,y,y') = 0 is an ODE. However, the term "differential algebraic system" has been applied by various authors [see, e.g., Griepentrog and Maerz (1986), Hairer & Wanner (1991), Stoer & Bulirsch (1993)] to mean a _decomposed_ system of the type: y'(x) = f(x, y(x), z(x)) 0 = g(x, y(x), z(x)) See also equation 7.2.17.7 in Stoer & Bulirsch (1993). There is a number of properties that are special to such "differential-algebraic systems". A number of these special properties are discussed in Gear (1988). Nothing dubious here. Just something a bit specialized, with a terminology that might be confusing to the uninitiated, especially in light of Petzold (1984). Hope this helps, -- Petr REFERENCES Gear, C.W. (1988) "Differential algebraic equation index transformation" SIAM J. Sci. Statist. Comput. 9, 39-47. Griepentrog, E.; Maerz, R. (1986) "Differential-Algebraic Equations and Their Numerical Treatment", Teubner, Leipzig. Hairer, E.; Wanner, G (1991) "Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems", Springer, Berlin (1991) Petzold, L. (1984) "ODE methods for the solution of differential algebraic systems" SIAM J. Numer. Anal. 21, 716-728. Stoer, J.; Bulirsch, R. (1993) "Introduction to Numerical Analysis", 2nd Ed., Springer, New York, pp. 494-497. _____________________________________________________________________ P e t r K u z m i c, Ph.D. mailto:pkuzmic@biokin.com BioKin Ltd. * Software and Consulting http://www.biokin.com