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Using DAE with DSolve
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Hi,
I am developing a set of ODEs and constraints to be solved using the dsolve(MoLSYS, numeric, method=rosenbrock_dae). The smallest system that I can set up to test my program is 3500 functions X 3500 equations. Unfortunately, dsolve doesn't return any result or error of any kind, even after an hour. Can anyone here please tell me the practical limit on the number of functions/equations that the DAE solver can handle?
Thank you,
PGK
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It depends on the index
If your system of DAEs has index larger than 2, there is essentially no hope of solving it with that method. In that case, the only package I know that can handle it is Ned Nedialkov's DAETS package. If your system is of index 1, then Maple should be able to get somewhere with it. Are you able to post a worksheet with a 'test' system?
Index of system
Hi Jacques,
Thank you for your reply, and for suggesting an alternative DAETS package. It might be necessary to use it as the project matures.
If by index you mean the order of the derivatives used, then I can tell you that they are all first order, and in fact the system is actually fairly simple. Unfortunately, I cannot post the code at this point because of non-disclosure agreements.
There is one change I need to make to the worksheet which might actually improve the prospects of the system being solved. I will report back a little later.
Thanks for you help,
PGK
index
No, the index is not the order. For a DAE, it rougly corresponds to the (minimum) number of derivatives you have to take of your system before you are able to transform it to a (larger) system of ODEs. It measures how 'implicit' your system is, and how difficult the problem of finding good initial starting points is.
Hi Jacques
Being new here, I didn't post my replies to you correctly. Sorry about that. I have added two new comments in reply to your helpful posts.
Thank you,
PGK
Hi Jacques
Being new here, I didn't post my replies to you correctly. Sorry about that. I have added two new comments in reply to your helpful posts.
Thank you,
PGK
Index
Hi Jacques,
Thank you for that clarification. Fortunately, all of the variables that appear in the set of constraint equations are linear. If I understand the procedure for converting the constraints into ODEs correctly, then the index would be one.
Unfortunately, the there are 30 constraint equations in only 27 functions, therefore, I believe Maple is having some trouble.
Thanks,
PGK
Consistency?
If you have 30 linear constraints in 27 functions, either 3 of them are redundant or your system is inconsistent. Note that redundant constraints would also cause most numerical methods difficulties.
Therein lies the problem
Hi Jacques,
Indeed, I am now certain that that is the cause of the problem. There is no expectation that DAE will be able to tackle the system of equations in its present form. There is a solution that my colleges and I worked out late last night that will allow us to express the problem differently in terms of 27 linear constraints and 27 functions. That is a great improvement on the system I have been working with so far.
I will be silent for a week or so while I work out the new details of the problem. But I will return with some updates.
Thank you for taking the time to give me help.
Best wishes,
PGK
Update on Progress
I believe my system of equations can be solved; but to do that, I need to use the appropriate algorythm. Today, I received a copy of what promises to be a very helpful book, _Numerical Solution of Initial-Value Problems in Differential-Algebraic Equatins_, by K. E. Brenan, S. L. Campbell, and L. R. Petzold. The book explains many of the important ideas such as the meaning of "index" as well as providing insight into various numerical methods and their applications.
Thanks,
PGK