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---------- X-Sun-Data-Type: text X-Sun-Data-Description: text X-Sun-Data-Name: text X-Sun-Charset: us-ascii X-Sun-Content-Lines: 44 -------------------------------------------------------------------------------- directly from my Sun workstation ULTRA 1 under SunOS 5.5.1 and CDE V 1.0.2 -------------------------------------------------------------------------------- An alle Mathematica-Kundigen ! Stuttgart, den 14. Januar 1999 Numerische Simulation einer elektrischen Leitung ------------------------------------------------ Eine elektrische Leitung werde durch die Leitungsgleichungen im Zeitbereich beschrieben. Diese Leitung werde von einer Spannungsquelle Ug[t] ueber einen Widerstand Rg getrieben und sei am anderen Ende bei xl mit dem Widerstand Rload belastet. NDSolve fuer ein System partieller Differential-Gleichungen ----------------------------------------------------------- Dieses Problem fuehrt auf ein System partieller Differential-Gleichungen, das ich versuchte, mit NDSolve zu loesen. Leider klappt es nicht. Das entsprechende Notebook "leitung_dmug.nb" haenge ich an diese Mail an. Woran liegt das ? Vielen Dank fuer jeden Hinweis ! Mit freundlichen Gruessen Gunter Woysch File : mail_99/dmug_991014_email_to -------------------------------------------------------------------------------- Dr. G. Woysch, Alcatel Telecom , ASIC Technology and Qualification Alcatel SEL AG , Dept. ZFZ/WH, D 70430 Stuttgart, Germany Phone +49 711 821-32176 Fax +49 711 821-32455 email gwoysch@rcs.sel.de -------------------------------------------------------------------------------- ---------- X-Sun-Data-Type: default X-Sun-Data-Description: default X-Sun-Data-Name: leitung_dmug.nb X-Sun-Charset: us-ascii X-Sun-Content-Lines: 343 (*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 3.0, MathReader 3.0, or any compatible application. The data for the notebook starts with the line of 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@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[ 8368, 254]*) (*NotebookOutlinePosition[ 9188, 282]*) (* CellTagsIndexPosition[ 9144, 278]*) (*WindowFrame->Normal*) Notebook[{ Cell["Elektrische Signale auf Verbindungsleitungen", "Title"], Cell["leitung_dmug.nb", "Section"], Cell[CellGroupData[{ Cell["\<\ Leitungsgleichungen im Zeitbereich \ \>", "Section"], Cell[CellGroupData[{ Cell[BoxData[ \(\(Ueqn\ = \n\t \(-\ \[PartialD]\_x\ u[x, t]\)\ == \ Rl\ i[x, t]\ + \ Ll\ \[PartialD]\_t\ i[x, t]\ \)\)], "Input"], Cell[BoxData[ RowBox[{ RowBox[{"-", RowBox[{ SuperscriptBox["u", TagBox[\((1, 0)\), Derivative], MultilineFunction->None], "[", \(x, t\), "]"}]}], "==", RowBox[{\(Rl\ i[x, t]\), "+", RowBox[{"Ll", " ", RowBox[{ SuperscriptBox["i", TagBox[\((0, 1)\), Derivative], MultilineFunction->None], "[", \(x, t\), "]"}]}]}]}]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(Ieqn\ = \n\t \(-\ \[PartialD]\_x\ i[x, t]\)\ == \ Gl\ u[x, t]\ + \ Cl\ \[PartialD]\_t\ u[x, t]\ \)\)], "Input"], Cell[BoxData[ \(General::"spell1" \( : \ \) "Possible spelling error: new symbol name \"\!\(Ieqn\)\" is similar to \ existing symbol \"\!\(Ueqn\)\"."\)], "Message"], Cell[BoxData[ RowBox[{ RowBox[{"-", RowBox[{ SuperscriptBox["i", TagBox[\((1, 0)\), Derivative], MultilineFunction->None], "[", \(x, t\), "]"}]}], "==", RowBox[{\(Gl\ u[x, t]\), "+", RowBox[{"Cl", " ", RowBox[{ SuperscriptBox["u", TagBox[\((0, 1)\), Derivative], MultilineFunction->None], "[", \(x, t\), "]"}]}]}]}]], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Parameter-Definition", "Section"], Cell[BoxData[ \(\(Ll\ = \ \ \ \ 1\ *10^\(-6\)\ \ \ \ \ \ \ \ ; \ \ (*\ Induktivitaetsbelag\ pro\ Laenge\ *) \n Cl\ = \ \ \ \ 1\ *\ 10^\(-12\)\ \ \ \ \ ; \ \ (*\ Kapazitaetsbelag\ pro\ Laenge\ *) \n Rl\ = \ 10\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ; \ \ (*\ Widerstandsbeleg\ pro\ Laenge\ \ *) \n Gl\ = \ \ \ 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ; \ \ \ (*\ Leitfaehigkeitsbelag\ pro\ Laenge\ *) \n Rg\ = \ 50\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ; \ \ \ (*\ Generatorinnenwiderstand\ *) \n Rload\ = 50\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ; \ \ \ (*\ Lastwiderstand\ *) \n xl\ = \ 1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ; \ \ \ \ (*\ Leitungslaenge\ *) \)\)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell["Treiber-Spannung", "Section"], Cell[CellGroupData[{ Cell[BoxData[ \(Ug[\ t\ ]\ = \ Sin[\ 2\ Pi\ 10^6\ t\ ]\)], "Input"], Cell[BoxData[ \(Sin[2000000\ \[Pi]\ t]\)], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["System partieller Differential-Gleichungen", "Section"], Cell[CellGroupData[{ Cell[BoxData[ \(solution\ = \ \n\t NDSolve[\n\t\t\ {\ Ueqn, \n\t\t\t\ \ Ieqn, \n\t\t\t\ \ \ u[x, 0] == 0, \n\t\t\t\ \ \ i[x, 0] == 0, \n\t\t\t\ \ \ u[0, t] == Ug[\ t\ ]\ - \ Rg\ i[0, t], \n\t\t\t\ \ \ u[1, t] == Rload\ \ *\ i[1, t]\n\t\t\ }, \n\t\t{\ u, i}, \ \n \t\t{\ x, \ 0, \ xl\ }, \ \n\t\t{t, \ 0, \ 10^\(-5\)\ }\ \n\t]\)], "Input"], Cell[BoxData[ \(Solve::"svars" \( : \ \) "Equations may not give solutions for all \"solve\" variables."\)], "Message"], Cell[BoxData[ \(NDSolve::"deql" \( : \ \) "The first argument must have both an equation and an initial \ condition."\)], "Message"], Cell[BoxData[ \(NDSolve::"deql" \( : \ \) "The first argument must have both an equation and an initial \ condition."\)], "Message"], Cell[BoxData[ RowBox[{"NDSolve", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", RowBox[{ SuperscriptBox["u", TagBox[\((1, 0)\), Derivative], MultilineFunction->None], "[", \(x, t\), "]"}]}], "==", RowBox[{\(10\ i[x, t]\), "+", FractionBox[ RowBox[{ SuperscriptBox["i", TagBox[\((0, 1)\), Derivative], MultilineFunction->None], "[", \(x, t\), "]"}], "1000000"]}]}], ",", RowBox[{ RowBox[{"-", RowBox[{ SuperscriptBox["i", TagBox[\((1, 0)\), Derivative], MultilineFunction->None], "[", \(x, t\), "]"}]}], "==", FractionBox[ RowBox[{ SuperscriptBox["u", TagBox[\((0, 1)\), Derivative], MultilineFunction->None], "[", \(x, t\), "]"}], "1000000000000"]}], ",", \(u[x, 0] == 0\), ",", \(i[x, 0] == 0\), ",", \(u[0, t] == \(-50\)\ i[0, t] + Sin[2000000\ \[Pi]\ t]\), ",", \(u[1, t] == 50\ i[1, t]\)}], "}"}], ",", \({u, i}\), ",", \({x, 0, 1}\), ",", \({t, 0, 1\/100000}\)}], "]"}]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(?? NDSolve\)], "Input"], Cell[BoxData[ \("NDSolve[eqns, y, {x, xmin, xmax}] finds a numerical solution to the \ ordinary differential equations eqns for the function y with the independent \ variable x in the range xmin to xmax. NDSolve[eqns, y, {x, xmin, xmax}, {t, \ tmin, tmax}] finds a numerical solution to the partial differential equations \ eqns. NDSolve[eqns, {y1, y2, ... }, {x, xmin, xmax}] finds numerical \ solutions for the functions yi."\)], "Print"], Cell[BoxData[ InterpretationBox[ StyleBox[\(Attributes[NDSolve]\ = \ {Protected}\n\ \n Options[NDSolve]\ = \ {AccuracyGoal\ -> \ Automatic, \ Compiled\ -> \ True, \ DifferenceOrder\ -> \ Automatic, \ InterpolationPrecision\ -> \ Automatic, \ MaxRelativeStepSize\ -> \ 1, \ MaxSteps\ -> \ Automatic, \ MaxStepSize\ -> \ Infinity, \ Method\ -> \ Automatic, \ PrecisionGoal\ -> \ Automatic, \ SolveDelayed\ -> \ False, \ StartingStepSize\ -> \ Automatic, \ StoppingTest\ -> \ None, \ WorkingPrecision\ -> \ 16}\), ShowStringCharacters->True, NumberMarks->True], InputForm[ Definition[ NDSolve]], Editable->True, AutoDelete->True]], "Print"] }, Open ]] }, Open ]] }, FrontEndVersion->"X 3.0", ScreenRectangle->{{0, 1152}, {0, 900}}, WindowSize->{520, 600}, WindowMargins->{{177, Automatic}, {Automatic, 102}}, PrintingPageRange->{Automatic, Automatic}, PrintingOptions->{"PaperSize"->{597.562, 842.375}, "PaperOrientation"->"Portrait", "Magnification"->1}, StyleDefinitions -> "Classroom.nb" ] (*********************************************************************** 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[1709, 49, 61, 0, 94, "Title"], Cell[1773, 51, 34, 0, 57, "Section"], Cell[CellGroupData[{ Cell[1832, 55, 63, 4, 101, "Section"], Cell[CellGroupData[{ Cell[1920, 63, 151, 3, 63, "Input"], Cell[2074, 68, 479, 14, 49, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[2590, 87, 151, 3, 63, "Input"], Cell[2744, 92, 175, 3, 39, "Message"], Cell[2922, 97, 479, 14, 49, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[3450, 117, 39, 0, 57, "Section"], Cell[3492, 119, 804, 14, 143, "Input"] }, Open ]], Cell[CellGroupData[{ Cell[4333, 138, 35, 0, 57, "Section"], Cell[CellGroupData[{ Cell[4393, 142, 72, 1, 47, "Input"], Cell[4468, 145, 56, 1, 47, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[4573, 152, 61, 0, 57, "Section"], Cell[CellGroupData[{ Cell[4659, 156, 394, 7, 239, "Input"], Cell[5056, 165, 133, 3, 39, "Message"], Cell[5192, 170, 143, 3, 39, "Message"], Cell[5338, 175, 143, 3, 39, "Message"], Cell[5484, 180, 1511, 37, 182, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[7032, 222, 43, 1, 47, "Input"], Cell[7078, 225, 444, 6, 135, "Print"], Cell[7525, 233, 815, 17, 167, "Print"] }, Open ]] }, Open ]] } ] *) (*********************************************************************** End of Mathematica Notebook file. ***********************************************************************) |