- #1
tau1777
- 30
- 0
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}]