4
$\begingroup$

Bug introduced in 10.4.0.0 or earlier and fixed in 11.0.1.

Compare the two solution sets below: in the first one (x == False), there are only 3 dependent variables while in the second one (x == True), a dependent algebraic variable is introduced as r[t] == 5 (converting the ODE to a DAE). A DAE often requires a different NDSolve method, here I used "EquationSimplification" -> {Automatic, "SimplifySystem" -> True} which messes up the solution order as is apparent from the plots.

ClearAll[t, R, A, P, r, x];
eq = {
      R'[t] == -.1 R[t],
      A'[t] == .1 A[t],
      P'[t] == 0,
      If[x, r[t] == Sin[t], Nothing],
      R[0] == 1, A[0] == 1, P[0] == 1
  };

sol1 = Block[{x = False}, 
   NDSolve[eq, {R, A, P}, {t, 0, 20}, DependentVariables -> {R, A, P}]];
sol2 = Block[{x = True}, 
   NDSolve[eq, {R, A, P, r}, {t, 0, 20}, DependentVariables -> {R, A, P, r}, 
    Method -> {"EquationSimplification" -> {Automatic, 
        "SimplifySystem" -> True}}]];

Grid[{
   LogPlot[#[t] /. sol1, {t, 0, 20}, PlotLabel -> #] & /@ {R, A, P},
   LogPlot[#[t] /. sol2, {t, 0, 20}, PlotLabel -> #] & /@ {R, A, P, r}
}]

Mathematica graphics

Can anyone reproduce this bug?

(Mathematica 10.4.0.0, Windows 7, 64bits)

TechSupport filed an internal report acknowledging the wrong order of output.

Improve this question
$\endgroup$
6
  • $\begingroup$ Removing DependentVariables -> ... in sol2 will also solve the issue. If r[t] is to be regarded as an algebraic function it may be more robust to provide initial conditions, e.g. { r[0] == 5, r[t] == 5 }. $\endgroup$
    – gwr
    Commented May 11, 2016 at 20:04
  • $\begingroup$ @gwr As a matter of fact, r can be any t-dependent function like Sin[t], I only left it as a constant for the sake of simplicity. I've edited it into the post. $\endgroup$
    – István Zachar
    Commented May 11, 2016 at 21:18
  • $\begingroup$ Ok, I see, but then the question has been a bit misleading. Also note that the plots do not match your question. :) $\endgroup$
    – gwr
    Commented May 11, 2016 at 21:28
  • $\begingroup$ @gwr Thanks for pointing out the discrepancy! My question was specifically about the reproducibility of this bug, though I have not yet added the tag [bug] as TS did not confirm it yet. $\endgroup$
    – István Zachar
    Commented May 11, 2016 at 21:50
  • $\begingroup$ Have you gotten any feedback with regard to the [bug] tag from TS yet? $\endgroup$
    – gwr
    Commented May 19, 2016 at 19:19

1 Answer 1

Reset to default
4
$\begingroup$

It seems that this might be a bug or maybe a weakness of the NDSolvemachinery. One can observe, that with the option "SimplifySystem" -> False the issue does not arise. In fact a lot of settings will cause no problem at all.

As far as I can see, the culprit is the option DependentVariables as it seems to influence the sequence of equation simplifications somehow. This can be seen here:

ClearAll[t, R, A, P, r, x];
With[
    {  eq = {
           R'[t] == -.1 R[t], A'[t] == .1 A[t], P'[t] == 0,
           r[t] == Sin[t],

           r[0] == Sin[0], R[0] == 1, A[0] == 1, P[0] == 1    
       },
       sequences = Permutations@{R, A, P, r} 
    },
    Module[
       {solutions, trials},
       solutions = Map[
           First @ NDSolve[
           eq, 
           {R, A, P, r}, 
           {t, 0, 20}, 
           DependentVariables -> #, (* use the actual permutation *)
           Method -> {"EquationSimplification" -> {Automatic, "SimplifySystem" -> True}}] &
           ,
           sequences
       ];
       trials = Transpose @ { sequences, solutions };
       Apply[
          Function[ {seq, sol} ,
            { 
               Map[ToString] /* StringJoin@ seq,
               Sequence @@ ( 
                 LogPlot[ #[t] /. sol, {t, 0, 20}, PlotLabel -> #, ImageSize -> Tiny, 
                 PlotTheme -> "Minimal"] & /@ {R, A, P, r}
               )
            }
          ],
          trials,
          1
       ] // Multicolumn[#, 3] &
    ]
]

Trials

We see that of the 24 possible sequences for the dependent variables only 4 produce the correct solution:

{A,P,R,r} , {A, P, r, R}, {A, r, P, R}, {r, A, P, R}

Update

This issue seems fixed now:

$Version

11.1.0 for Microsoft Windows (64-bit) (March 13, 2017)

The above code now produces the same results for all permutations of the sequence of variables as it should:

correct results

Improve this answer
$\endgroup$
5
  • $\begingroup$ I see, it all hinges on "SimplifySystem" -> True as with False everthing turns out ok. $\endgroup$
    – gwr
    Commented May 11, 2016 at 21:42
  • $\begingroup$ Yes, the internal simplification somehow rotates the list of variables by one to the left, regardless of the number of added algebraic functions (I've tried with more than one such variable). $\endgroup$
    – István Zachar
    Commented May 11, 2016 at 21:47
  • $\begingroup$ @IstvánZachar I do note, that it works out when the option DependentVariables is dropped? -- My gut feeling here is bug. $\endgroup$
    – gwr
    Commented May 11, 2016 at 21:48
  • 1
    $\begingroup$ To be honest, it works with any of the option-specifications being dropped : ) $\endgroup$
    – István Zachar
    Commented May 11, 2016 at 21:56
  • $\begingroup$ @IstvánZachar It seems that the option DependentVariablesindeed is the culprit, as the sequence given there influences the equation simplification as can be seen from my updated answer. $\endgroup$
    – gwr
    Commented May 12, 2016 at 9:48

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.