- #1

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## 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.

Any suggestions/comments about this errors and my PDEs are greatly appreciated. Thank you so much.

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}]

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.

Any suggestions/comments about this errors and my PDEs are greatly appreciated. Thank you so much.

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}]