Talk:Differential-algebraic system of equations

message: So this article is clearly directed at engineers and the style in which it is written is guiding engineers away from a body of literature available to them in mathematics (namely foliation theory and differential algebra). 
These theorems and constructions could potentially be helpful in their investigations. 
 
In particular a DAE in the sense of this article is just a collection of differential polynomials as polynomials are naturally included in the term ``differential polynomial. From here there are two natural ways to construct objects that people are interested in: via differential algebraic varieties, and via foliations (or more precisely exterior differential systems). 
I'm not sure what to do but there is a language problem. There shouldn't exist distinct article from algebraic differential equation and differential algebraic equation because it only serves to separate and confuse people who are searching for information that could be useful to them.   — Preceding unsigned comment added by DupuyTaylor (talk • contribs) 01:45, 9 December 2022 (UTC)
thread_title:  This Article Should be Refactored 

message: Istn't the first equation not a simple implicit ODE?  — Preceding unsigned comment added by 85.178.223.187 (talk) 11:22, 27 January 2014 (UTC)
thread_title:  First equation 

message: Modelica is not some software but a modeling language.
There are some programs which use this language such as SimulationX or Dymola.  —Preceding unsigned comment added by 84.179.9.10 (talk) 20:32, 11 September 2007 (UTC)
replies: text: It's essentially the number of times you have to differentiate some of the equations in the system until you can extract an ODE. This is the differentiation index and most of the times the perturbation index.  For the numerical treatment, also index 1 systems with explicit separation of algebraic and differental equations are fine. This is what the strangeness index and tractability index are about.--LutzL (talk) 18:47, 31 May 2008 (UTC)
thread_title:  Modelica is not a software 

message: Shouldn't Mathematica be included with the other programs? I am fairly certain it can easily manipulate DAEs. Either way, just a suggestion.  —Preceding unsigned comment added by PromisedProgress (talk • contribs) 20:23, 29 December 2008 (UTC)
replies: text: Could you please explain what capabilities you had in mind? Surely there will be numerical routines for index 1 and 2 systems. For general higher index systems, even the experts aren't exactly sure what a sensible symbolic manipulation of DAEs should consist of. And one needs some symbolic, index-reducing pre-processing, since numerics only works well for index 1 systems.--LutzL (talk) 14:32, 30 December 2008 (UTC)
thread_title: Mathematica

message: This isn't worth fretting much about, but the more common name in sources appears to use a dash as in "differential-algebraic equations". Also the title should probably use the plural "equations" because in order for the definition to be  interesting you need to have a mixture of algebraic and differential eq., i.e. have at least two equations in the system. 86.121.137.150 (talk) 21:35, 16 December 2014 (UTC)
thread_title:  Title 

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thread_title:  External links modified 

message: In the pendulum example, the last equation (algebraic constraint) is derived 3 times to get an explicit expression for each dependent variable (i.e., if I understood correctly, an ODEs system - please somebody clarify this in the Introduction, when talking about differences between ODEs and DAEs). Hence, a differentiation index of 3 is obtained. However, right below, it is written that the DAE has index 1. Can somebody please clarify this part? Are possibly those separate indexes (not properly defined in that case)?  — Preceding unsigned comment added by 131.175.28.194 (talk) 13:29, 17 May 2018 (UTC)
thread_title:  Examples 

message: A method called Sigma-method is presented to analyze DAEs. However, no conclusions are drawn from this analysis. How is the matrix Sigma useful/informative? Also, the balck "dot" which appears on top right of some numbers is not a well-defined symbol, and somebody should please clarify its meaning.  — Preceding unsigned comment added by 131.175.28.194 (talk) 13:28, 18 May 2018 (UTC)
thread_title: Structural analysis for DAEs

message: The article currently has a warning suggesting that the lead section is too long.  Perhaps the discussion about the distinction between DAEs and ODEs could be moved to its own section under the heading "Distinction between DAEs and ODEs"? Zor Quatre (talk) 20:01, 9 June 2023 (UTC)
thread_title:  Shortening lead section 

message: The definition of ODE used in this article is less general than the one used in the Ordinary differential equation page. There, DAEs are a special case of ODEs, as ODEs are not required to be equivalent to an explicit ODE. One can read in that page:
« More generally, an implicit ordinary differential equation of order n takes the form:
:F\left(x, y, y', y,\ \ldots,\ y^{(n)}\right) = 0 »
Thus i suggest rewriting the paragraphs comparing ODE and DAE, seeing DAEs as a special class of implicit ODEs. Adding that one usually restricts the term "ODE" to mean "explicit ODE", and that some DAEs are not equivalent to any explicit ODE. Plm203 (talk) 08:32, 8 May 2024 (UTC)
thread_title:  Conflict with the usual definition of ODE