Re: I have put "==" in every equation I have in NDSolve, why it keeps telling me they are not equations
- To: mathgroup at smc.vnet.net
- Subject: [mg44587] Re: I have put "==" in every equation I have in NDSolve, why it keeps telling me they are not equations
- From: drbob at bigfoot.com (Bobby R. Treat)
- Date: Sat, 15 Nov 2003 02:05:15 -0500 (EST)
- References: <bmqplo$rhb$1@smc.vnet.net> <bmt8eg$87l$1@smc.vnet.net> <3FB43093.4000104@physics.ucsb.edu> <bp299p$38b$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
My Mathematica 5.0 kernel doesn't seem to have that problem. I'd suggest eliminating the new-lines embedded in the equation list, as that can sometimes lead to problems. I get this error instead: NDSolve::underdet: There are more dependent variables, {p[y, t, x], u[y, t, \ x], v[y, t, x]}, than equations, so the system is underdetermined. Bobby Xiaochao Xu <xiaochao at physics.ucsb.edu> wrote in message news:<bp299p$38b$1 at smc.vnet.net>... > NDSolve::deqn: "Equation or list of equations expected instead of 0 in the \ > first argument > > ------------------------------------------------------------------------ > > (************** Content-type: application/mathematica ************** > CreatedBy='Mathematica 5.0' > > Mathematica-Compatible Notebook > > This notebook can be used with any Mathematica-compatible > application, such as Mathematica, MathReader or Publicon. The data > for the notebook starts with the line containing stars above. > > To get the notebook into a Mathematica-compatible application, do > one of the following: > > * Save the data starting with the line of stars above into a file > with a name ending in .nb, then open the file inside the > application; > > * Copy the data starting with the line of stars above to the > clipboard, then use the Paste menu command inside the application. > > Data for notebooks contains only printable 7-bit ASCII and can be > sent directly in email or through ftp in text mode. Newlines can be > CR, LF or CRLF (Unix, Macintosh or MS-DOS style). > > NOTE: If you modify the data for this notebook not in a Mathematica- > compatible application, you must delete the line below containing > the word CacheID, otherwise Mathematica-compatible applications may > try to use invalid cache data. > > For more information on notebooks and Mathematica-compatible > applications, contact Wolfram Research: > web: http://www.wolfram.com > email: info at wolfram.com > phone: +1-217-398-0700 (U.S.) > > Notebook reader applications are available free of charge from > Wolfram Research. > *******************************************************************) > > (*CacheID: 232*) > > > (*NotebookFileLineBreakTest > NotebookFileLineBreakTest*) > (*NotebookOptionsPosition[ 8798, 217]*) > (*NotebookOutlinePosition[ 9438, 239]*) > (* CellTagsIndexPosition[ 9394, 235]*) > (*WindowFrame->Normal*) > > > > Notebook[{ > > Cell[CellGroupData[{ > Cell[BoxData[ > \(c = 100.0; \[Omega] = 100.0\)], "Input"], > > Cell[BoxData[ > \(100.`\)], "Output"] > }, Open ]], > > Cell[CellGroupData[{ > > Cell[BoxData[ > \(NDSolve[{\[PartialD]\_t u[t, x, y] + > Cos[x]*Sin[y]*\[PartialD]\_x u[t, x, y] - > Sin[x]*Cos[y]*\[PartialD]\_y u[t, x, y] - > Sin[x]*Sin[y]*u[t, x, y] + Cos[x]*Cos[y]*v[t, x, y] - > Sin[x]*Cos[x]/c2* > p[t, x, y] == \(-\[PartialD]\_x p[t, x, > y]\), \ \[IndentingNewLine]\[IndentingNewLine]\[PartialD]\_t > v[t, x, y] + Cos[x]*Sin[y]*\[PartialD]\_x v[t, x, y] - > Sin[x]*Cos[y]*\[PartialD]\_y v[t, x, y] - > Cos[x]*Cos[y]*u[t, x, y] + Sin[x]*Sin[y]*v[t, x, y] - > Sin[y]*Cos[y]/c2* > p[t, x, y] == \(-\[PartialD]\_y p[t, x, > y]\), \[IndentingNewLine]\[IndentingNewLine]\[PartialD]\_t p[ > t, x, y] + > c2*\((\[PartialD]\_x u[t, x, y] + \[PartialD]\_y v[t, x, y])\) + > Cos[x]*Sin[y]*\[PartialD]\_x p[t, x, y] == > Sin[x]*Cos[ > y]*\[PartialD]\_y p[t, x, > y], \[IndentingNewLine]\[IndentingNewLine]u[0, x, y] \[Equal] > 0, v[0, x, y] == 0, p[0, x, y] == 0, > u[t, 0, y] == > Cos[\[Omega]*t]*\((1 - Exp[\(-t\)/0.1])\)*DiracDelta[y]\ , > v[t, 0, y] == 0, > p[t, 0, y] == > Sin[\[Omega]*t]*\((1 - Exp[\(-t\)/0.1])\)*DiracDelta[y], \ > u[t, x, 1000] == 0, v[t, x, 1000] == 0, p[t, x, 1000] == 0, > u[t, x, \(-1000\)] == 0, v[t, x, \(-1000\)] == 0, > p[t, x, \(-1000\)] == 0}, {u, v, p}, {x, 0, 100}, {y, \(-1\), 1}, {t, > 0, 1000}]\)], "Input"], > > Cell[BoxData[ > RowBox[{\(NDSolve::"deqn"\), \(\(:\)\(\ \)\), "\<\"Equation or list of \ > equations expected instead of \\!\\(0\\) in the first argument \\!\\({\\(\ > \[LeftSkeleton] 1 \[RightSkeleton]\\)}\\). \\!\\(\\*ButtonBox[\\\"More\ > \[Ellipsis]\\\", ButtonStyle->\\\"RefGuideLinkText\\\", ButtonFrame->None, \ > ButtonData:>\\\"NDSolve::deqn\\\"]\\)\"\>"}]], "Message"], > > Cell[BoxData[ > RowBox[{"NDSolve", "[", > RowBox[{ > RowBox[{"{", > RowBox[{ > RowBox[{ > > RowBox[{\(\(-0.0001`\)\ Cos[x]\ p[t, x, y]\ Sin[x]\), > "-", \(Sin[x]\ Sin[y]\ u[t, x, y]\), > "+", \(Cos[x]\ Cos[y]\ v[t, x, y]\), "-", > RowBox[{\(Cos[y]\), " ", \(Sin[x]\), " ", > RowBox[{ > SuperscriptBox["u", > TagBox[\((0, 0, 1)\), > Derivative], > MultilineFunction->None], "[", \(t, x, y\), "]"}]}], > "+", > RowBox[{\(Cos[x]\), " ", \(Sin[y]\), " ", > RowBox[{ > SuperscriptBox["u", > TagBox[\((0, 1, 0)\), > Derivative], > MultilineFunction->None], "[", \(t, x, y\), "]"}]}], > "+", > RowBox[{ > SuperscriptBox["u", > TagBox[\((1, 0, 0)\), > Derivative], > MultilineFunction->None], "[", \(t, x, y\), "]"}]}], > "\[Equal]", > RowBox[{"-", > RowBox[{ > SuperscriptBox["p", > TagBox[\((0, 1, 0)\), > Derivative], > MultilineFunction->None], "[", \(t, x, y\), "]"}]}]}], > ",", > RowBox[{ > > RowBox[{\(\(-0.0001`\)\ Cos[y]\ p[t, x, y]\ Sin[y]\), > "-", \(Cos[x]\ Cos[y]\ u[t, x, y]\), > "+", \(Sin[x]\ Sin[y]\ v[t, x, y]\), "-", > RowBox[{\(Cos[y]\), " ", \(Sin[x]\), " ", > RowBox[{ > SuperscriptBox["v", > TagBox[\((0, 0, 1)\), > Derivative], > MultilineFunction->None], "[", \(t, x, y\), "]"}]}], > "+", > RowBox[{\(Cos[x]\), " ", \(Sin[y]\), " ", > RowBox[{ > SuperscriptBox["v", > TagBox[\((0, 1, 0)\), > Derivative], > MultilineFunction->None], "[", \(t, x, y\), "]"}]}], > "+", > RowBox[{ > SuperscriptBox["v", > TagBox[\((1, 0, 0)\), > Derivative], > MultilineFunction->None], "[", \(t, x, y\), "]"}]}], > "\[Equal]", > RowBox[{"-", > RowBox[{ > SuperscriptBox["p", > TagBox[\((0, 0, 1)\), > Derivative], > MultilineFunction->None], "[", \(t, x, y\), "]"}]}]}], > ",", > RowBox[{ > RowBox[{ > RowBox[{\(Cos[x]\), " ", \(Sin[y]\), " ", > RowBox[{ > SuperscriptBox["p", > TagBox[\((0, 1, 0)\), > Derivative], > MultilineFunction->None], "[", \(t, x, y\), "]"}]}], > "+", > RowBox[{"10000.`", " ", > RowBox[{"(", > RowBox[{ > RowBox[{ > SuperscriptBox["v", > TagBox[\((0, 0, 1)\), > Derivative], > MultilineFunction->None], "[", \(t, x, y\), "]"}], > "+", > RowBox[{ > SuperscriptBox["u", > TagBox[\((0, 1, 0)\), > Derivative], > MultilineFunction->None], "[", \(t, x, y\), "]"}]}], > ")"}]}], "+", > RowBox[{ > SuperscriptBox["p", > TagBox[\((1, 0, 0)\), > Derivative], > MultilineFunction->None], "[", \(t, x, y\), "]"}]}], > "\[Equal]", > RowBox[{\(Cos[y]\), " ", \(Sin[x]\), " ", > RowBox[{ > SuperscriptBox["p", > TagBox[\((0, 0, 1)\), > Derivative], > MultilineFunction->None], "[", \(t, x, y\), "]"}]}]}], > ",", \(u[0, x, y] \[Equal] 0\), ",", \(v[0, x, y] \[Equal] 0\), > ",", \(p[0, x, y] \[Equal] 0\), > ",", \(u[t, 0, > y] \[Equal] \((1 - \[ExponentialE]\^\(\(-10.`\)\ t\))\)\ Cos[ > 100.`\ t]\ DiracDelta[y]\), ",", \(v[t, 0, y] \[Equal] 0\), > ",", \(p[t, 0, > y] \[Equal] \((1 - \[ExponentialE]\^\(\(-10.`\)\ t\))\)\ \ > DiracDelta[y]\ Sin[100.`\ t]\), ",", "0", ",", "0", ",", "0", ",", "0", ",", > "0", ",", "0"}], "}"}], ",", \({u, v, p}\), ",", \({x, 0, 100}\), > ",", \({y, \(-1\), 1}\), ",", \({t, 0, 1000}\)}], "]"}]], "Output"] > }, Open ]] > }, > FrontEndVersion->"5.0 for Macintosh", > ScreenRectangle->{{38, 1280}, {0, 1002}}, > WindowSize->{1086, 806}, > WindowMargins->{{35, Automatic}, {Automatic, 64}} > ] > > (******************************************************************* > Cached data follows. If you edit this Notebook file directly, not > using Mathematica, you must remove the line containing CacheID at > the top of the file. The cache data will then be recreated when > you save this file from within Mathematica. > *******************************************************************) > > (*CellTagsOutline > CellTagsIndex->{} > *) > > (*CellTagsIndex > CellTagsIndex->{} > *) > > (*NotebookFileOutline > Notebook[{ > > Cell[CellGroupData[{ > Cell[1776, 53, 60, 1, 27, "Input"], > Cell[1839, 56, 39, 1, 27, "Output"] > }, Open ]], > > Cell[CellGroupData[{ > Cell[1915, 62, 1559, 29, 224, "Input"], > Cell[3477, 93, 372, 5, 21, "Message"], > Cell[3852, 100, 4930, 114, 135, "Output"] > }, Open ]] > } > ] > *) > > > > (******************************************************************* > End of Mathematica Notebook file. > *******************************************************************)