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Use NDSolve with conditional coefficients?

Iuval Clejan
Posted 10 years ago

I have two coupled first order non-linear ODEs, which have coefficients that depend on the functions and their first derivatives. I tried a few conditionals such as If and Piecewise, but NDSolve claims that: "NDSolve::ndnum: Encountered non-numerical value for a derivative at t == 0.`. >>".

This must come up all the time in control systems--do I need to use that formalism (I only have version 8 home edition), or can I get "under the hood" of NDSolve to do this? It works if A is defined without conditions, but I need to find the best A (according to different utility functions) subject to certain constraints.

A[i_, h_] := Piecewise[{{1 - i*0.1, h >= 0.0}, {0, h < 0}}]
sol[i_] := 
 NDSolve[{n'[t] == 
    kg + n[t] (A[i, hc - hi[y[t], y'[t]]] (qc - qi[hi[y[t], y'[t]]]) +
         qi[hi[y[t], y'[t]]] - 1), 
   y'[t] == (p[i, y[t], y'[t]] - A[i, hc - hi[y[t], y'[t]]]) b, 
   n[0] == ninit, y[0] == 1}, {n[t], y[t], n'[t], y'[t]}, {t, 0, 100}]
POSTED BY: Iuval Clejan
7 Replies
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Bill Simpson
Bill Simpson
Posted 10 years ago

Now I understand. Again we have been bitten by the desktop publishing done to posts by the forum software.
POSTED BY: Bill Simpson
Iuval Clejan
Iuval Clejan
Posted 10 years ago

That is not the difference that actually exists. My code does have the underlines, it's an artefact of copying from Mathematica and pasting into the browser somehow.
POSTED BY: Iuval Clejan
Bill Simpson
Bill Simpson
Posted 10 years ago

Look closely at the differences between yours

hi[y, yp] := k1 y + k2 Max[0, yp]; 
A[i, h] := Piecewise[{{1 - i*0.1, h >= 0.0}, {0, h < 0}}]; 
p[i, y, yp_] := 1;

and mine

hi[y_, yp_] := k1 y + k2 Max[0, yp];
A[i_, h_] := Piecewise[{{1 - i*0.1, h >= 0.0}, {0, h < 0}}];
p[i_, y_, yp_] := 1;

which can often make a very large difference to Mathematica.

As for the error message from Mathematica, I expect this is the result of introducing things with abrupt changes like Max and Piecewise into NDSolve. Someone with more experience with NDSolve than I have will need to address that issue.
POSTED BY: Bill Simpson
Iuval Clejan
Iuval Clejan
Posted 10 years ago

I need to learn how to post in nice format like you did--I see that option now. But the input looks the same as mine, except for the formatting here? So you get the same error I do, with some preliminary errors from tddisc, which is probably because you have a newer version. What does it mean? Why is there a problem for a certain range of k2?
POSTED BY: Iuval Clejan
Bill Simpson
Bill Simpson
Posted 10 years ago

Fix a few things

ninit = 10; qc = 0.2; hc = 0.1; kg = 7; k1 = 0.01; k2 = -0.01; b = 1; a = 0.79;
qi[hi_] := (Tanh[hi - a] + 1)/2;
hi[y_, yp_] := k1 y + k2 Max[0, yp]; 
A[i_, h_] := Piecewise[{{1 - i*0.1, h >= 0.0}, {0, h < 0}}]; 
p[i_, y_, yp_] := 1; 
sol[i_] := NDSolve[{n'[t]==kg+n[t] (A[i, hc- hi[y[t], y'[t]]] (qc-qi[hi[y[t], y'[t]]])+qi[hi[y[t],y'[t]]]-1), 
   y'[t] == (p[i, y[t], y'[t]] - A[i, hc - hi[y[t], y'[t]]]) b, 
   n[0] == ninit, y[0] == 1}, {n[t], y[t], n'[t], y'[t]}, {t, 0, 100}];
sol0 = sol[0]

which results in

During evaluation of In[1]:= NDSolve::tddisc: NDSolve cannot do a discontinuity replacement for event surfaces that depend only on time. >>

During evaluation of In[1]:= NDSolve::tddisc: NDSolve cannot do a discontinuity replacement for event surfaces that depend only on time. >>

During evaluation of In[1]:= NDSolve::ndnum: Encountered non-numerical value for a derivative at t == 0.`. >>
POSTED BY: Bill Simpson
Iuval Clejan
Iuval Clejan
Posted 10 years ago
POSTED BY: Iuval Clejan
Bill Simpson
Bill Simpson
Posted 10 years ago
POSTED BY: Bill Simpson
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