# Mathematica NDsolve error, ndode?

• Mathematica

## Main Question or Discussion Point

Hi all,

So I'm trying to solve, what I think are three coupled PDEs with NDSolve and it keeps giving me

NDSolve::ndode: Input is not an ordinary differential equation. >>

as an error. I don't quite understand why?

These are my PDEs for anyone that's interested. I will try to pretty them up in a separate post. I'm kind of in a rush right now.

sol = NDSolve[

{
D[\[Delta]ur[r, \[Theta]], r] + D[\[Delta]u\[Theta][ r, \[Theta]], \[Theta]] ==
(ut/ rmd[r, \[Theta]] *(\[Sigma] - m*\[CapitalOmega])*\[Delta]rmd [
r, \[Theta]] ) - (2/r +
1/rmd[r, \[Theta]]* drmdr[r, \[Theta]] +
2*dalphar[r, \[Theta]] + dbetar[r, \[Theta]] +
dnur[r, \[Theta]])*\[Delta]ur[
r, \[Theta]] - (Cot[\[Theta]] +
1/rmd[r, \[Theta]]*drmd\[Theta][r, \[Theta]] +
2*dalpha\[Theta][r, \[Theta]] + dbeta\[Theta][r, \[Theta]] +
dnu\[Theta][r, \[Theta]])*\[Delta]u\[Theta][
r, \[Theta]] + (\[Sigma]*F[r, \[Theta]] -
m)*\[Delta]u\[CurlyPhi][r, \[Theta]],

D[\[Delta]p[r, \[Theta]],
r] == (((\[Epsilon] + p)*ut)/
Exp [-2 \[Alpha]])*(((1 /(\[Epsilon] + p)^2) *
Exp [-2 \[Alpha]]/ut *
D[p[r, \[Theta]],
r]*(\[Delta]\[Epsilon][r, \[Theta]] + \[Delta]p[
r, \[Theta]])) - (\[Sigma] -
m*\[CapitalOmega])*\[Delta]ur[
r, \[Theta]] + (Exp[2 \[Beta] - 2 \[Alpha]]*
r^2* (Sin[\[Theta]])^2* ( \[CapitalOmega] - \[Omega][r, q])*
D[Log [F[r, \[Theta]]], r]* \[Delta]u\[CurlyPhi][
r, \[Theta]])),

D[\[Delta]p[
r, \[Theta]], \[Theta]] == (((\[Epsilon] + p)*r^2 * ut )/
Exp [-2 \[Alpha]])*((1 /(\[Epsilon] + p)^2 *
Exp [-2 \[Alpha]]/r^2*ut *
D[p[r, \[Theta]], \[Theta]]*(\[Delta]\[Epsilon][
r, \[Theta]] + \[Delta]p[r, \[Theta]]) - (\[Sigma] -
m*\[CapitalOmega])*\[Delta]u\[Theta][
r, \[Theta]] + (Exp[2 \[Beta] - 2 \[Alpha]]*
r^2* (Sin[\[Theta]])^2* ( \[CapitalOmega] - \[Omega][
r, \[Theta]])*
D[Log[ F[r, \[Theta]]], r])* \[Delta]u\[CurlyPhi][
r, \[Theta]])),

(*Boundary Conditions*)
\[Delta]\[Theta][1, \[Theta]] ==
0, \[Delta]ur[1, \[Theta]] == \[Delta]p[
1, \[Theta]] == \[Delta]\[Theta][r, 1] == \[Delta]ur[r,
1] == \[Delta]p[r, 1] ==
0, -I*\[Gamma]1*\[Delta]p[128, \[Theta]] + \[Delta]ur[
128, \[Theta]]*
Evaluate[D[\[Delta]p[128, \[Theta]], r]] + \[Delta]u\[Theta][
128, \[Theta]]*
Evaluate[D[\[Delta]p[128, \[Theta]], \[Theta]]] ==
0},

(*what I'm solving for, and the bounds*)
{\[Delta]p, \[Delta]ur, \[Delta]u\[Theta]}, {r, 1,
128}, {\[Theta], 1, 64}]

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I cannot tell from what you have shown whether
1: you have left out a variety of function definitions and variable assignments or
2: you are thinking NDSolve is going to give you a numeric solution with those undefined.
If you have defined and assigned all those values so this is strictly a numerical solution process then perhaps the problem lies in what you have not included. If you have not defined and assigned then this is a common problem, people expecting a numerical integration solution when they arbitrary variables or, even worse, arbitrary functions in what they pass to NDSolve nor NSolve.

From a different direction, it appears that for years people have asked why they are getting this warning message
and there does not appear to be a simple clear answer to that question.

Does any of this seem to relate to your question?

Hi Bill,

I'm very sorry about the lack of explanation. I have added a .pdf file with an explanation of the variables and I've made the eqs nicer.

I did try looking it up on the google. And I reached the conclusion that no one really knows what causes this error. That's one of the reason's I'm putting it up here. Because I think that I just need someone experience with Mathematica to look at it.

Thanks again for even looking at this mess. I truly appreciate it.

#### Attachments

• 49 KB Views: 143
It isn't easy to import the equations out of a pdf document back into a notebook.

Would it be possible for you to take all your data and crunch it down to
Alpha=youractualvalue;
CapitalOmega=youractualvalue;
etc
for all the variables that you actually have values for
and attach the resulting notebook to your next post?

That would let me try to reproduce what you are doing with the actual values you have.

Hi Bill,

Really sorry about the late reply. I wasn't sure how to respond. I don't think I can give out the data as this pertains to current research being done.

I have made some progress on the problem. And I believe one of the problems I was having with Mathematica was not with Mathematica at all. I was just trying to have it solve a problem that was mathematically ill-posed. So its no wonder it failed.

Anyways, thanks for all the help. Sorry again about the super-late reply.