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| author | Sven Eisenhauer <sven@sven-eisenhauer.net> | 2023-11-10 15:11:48 +0100 |
|---|---|---|
| committer | Sven Eisenhauer <sven@sven-eisenhauer.net> | 2023-11-10 15:11:48 +0100 |
| commit | 33613a85afc4b1481367fbe92a17ee59c240250b (patch) | |
| tree | 670b842326116b376b505ec2263878912fca97e2 /Bachelor/Numerische Mathematik/Num05Aufg4B.nb | |
| download | Studium-master.tar.gz Studium-master.tar.bz2 | |
Diffstat (limited to 'Bachelor/Numerische Mathematik/Num05Aufg4B.nb')
| -rw-r--r-- | Bachelor/Numerische Mathematik/Num05Aufg4B.nb | 1437 |
1 files changed, 1437 insertions, 0 deletions
diff --git a/Bachelor/Numerische Mathematik/Num05Aufg4B.nb b/Bachelor/Numerische Mathematik/Num05Aufg4B.nb new file mode 100644 index 0000000..e9223fd --- /dev/null +++ b/Bachelor/Numerische Mathematik/Num05Aufg4B.nb @@ -0,0 +1,1437 @@ +(************** Content-type: application/mathematica **************
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+ FontColor->RGBColor[1, 0, 0]]}]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[
+ RowBox[{" ",
+ RowBox[{
+ RowBox[{\(index\ = \ \ 19\ ;\), " ",
+
+ StyleBox[\( (*\
+ Nummer\ des\ zu\ \[ADoubleDot]ndernden\ Punktes\ \((\
+ index\ )\)\ eingeben\ *) \),
+ FontColor->RGBColor[1, 0, 0]]}], " ", "\n", " ",
+ RowBox[{
+ RowBox[{"If", "[",
+ RowBox[{\(sch \[Equal] "\<K\>"\), ",",
+ RowBox[{"If", "[",
+
+ RowBox[{\(index \[GreaterEqual] 0\ And\ index \[LessEqual]
+ m\), ",",
+ RowBox[{"{", " ",
+
+ RowBox[{\(xp[index] = \ \ \ \(-3.90\)\),
+ " ",
+ StyleBox[\( (*\ xp[i]\ eingeben\ *) \),
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox[";",
+ FontColor->RGBColor[1, 0, 0]], "\[IndentingNewLine]",
+ " ", \(yp[index] = \ \ \ \(-0.5\)\)}],
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 0]]}]],
+ StyleBox[\( (*\ yp[i]\ eingeben\ *) \),
+ FontColor->RGBColor[1, 0, 0]],
+ StyleBox["}",
+ FontColor->RGBColor[1, 0, 0]]}]}],
+ StyleBox["]",
+ FontColor->RGBColor[1, 0, 0]]}]}],
+ StyleBox["]",
+ FontColor->RGBColor[1, 0, 0]]}],
+ StyleBox[";",
+ FontColor->RGBColor[1, 0, 0]]}]}]}]], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox["(*",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[
+ RowBox[{
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]]}]],
+ RowBox[{
+ StyleBox[\(St\[UDoubleDot]tzpunkte\ \ \ 0\),
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[",",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["..",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[",",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["m",
+ "Subsection",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[",",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[\(nach\ dem\ Einf\[UDoubleDot]gen\ von\ Punkten\),
+ FontColor->RGBColor[1, 0, 1]]}],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["*)",
+ FontColor->RGBColor[1, 0, 1]]}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ \(If[sch \[Equal] "\<K\>",
+ If[index \[GreaterEqual] 0\ And\ index \[LessEqual]
+ m, \ \ \ \[IndentingNewLine]TableForm[
+ Table[{ind = PaddedForm[i, 2], "\< xp[\>", ind, "\<] = \>",
+ PaddedForm[xp[i], {3, 2}], \[IndentingNewLine]"\< yp[\>",
+ ind, "\<] = \>", PaddedForm[yp[i], {3, 2}]}, {i, 0, m}],
+ TableSpacing \[Rule] {1, 0}]]]\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]]}]],
+ StyleBox[\( (*\ \ \ \ \ \ \ \ Bereitstellen\ des\ Parameters\ tp\ f\
+\[UDoubleDot]r\ die\ m\ St\[UDoubleDot]tzpunkte\ \ \ \ \ \ \ \ \ *) \),
+ "Subsection",
+ FontColor->RGBColor[1, 0, 0]]}]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[
+ \(\(\(\ \)\(\(tp[0] = 0;\)\[IndentingNewLine]
+ Do[{Delt[k - 1] =
+ Sqrt[\((xp[k] - xp[k - 1])\)^2 + \((yp[k] - yp[k - 1])\)^2],
+ tp[k] = tp[k - 1] + Delt[k - 1]}, {k, 1, m}]\)\)\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]]}]],
+ StyleBox[\( (*\ \ \ \ \ \ \ \ St\[UDoubleDot]tzstellen\ f\[UDoubleDot]r\
+\ die\ Parameterdarstellung\ der\ Ellipse\ \ \ \ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]], "\[IndentingNewLine]",
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]]}]],
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ und\ Bereitstellen\ des\ Parameters\
+\ tj, \ \((\ j, \ 0, \ nd\ )\)\ \ \ \ \ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]]}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ \(\(nd = 400;\)\)], "Input"],
+
+Cell[BoxData[
+ \(Do[{tj[j] = tp[0] + j*\((tp[m] - tp[0])\)/nd, \
+ tel[j] =
+ 8. *ArcTan[1]/nd*
+ j, \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ xel[j] = \(-\ 4\)*Cos[tel[j]],
+ yel[j] = 3*Sin[tel[j]]}, {j, 0, nd}]\)], "Input"],
+
+Cell[BoxData[
+ \(<< Graphics`Colors`\)], "Input"],
+
+Cell[BoxData[
+ \(\(liste1 = {Red, HotPink, Green, Apricot, Brown, DarkGreen, Cobalt,
+ Brick, Orange, Magenta, IndianRed, ForestGreen};\)\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]]}]],
+ StyleBox[\( (*\ \ \ \ \ Plotten\ der\ Ellipse\ \ x\ = \ \(4*
+ cos \((t)\)\ \ und\ \ y\ = \
+ 3*sin \((t)\)\)\ \ \ \ \ \ \ \ \ \ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]]}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ \(ellipsplot =
+ ListPlot[Table[{xel[j], yel[j]}, {j, 0, nd}],
+ PlotJoined\ -> \ True, \n\t
+ PlotRange -> {{\(-5\), 5}, {\(-4\), 4}}, \tPlotStyle -> Brown,
+ AspectRatio -> 0.5, AxesLabel -> {"\<> x\>", "\< ^ y\>"}]\)], "Input"],
+
+Cell[BoxData[
+ \(punktplot =
+ ListPlot[Table[{xp[k], yp[k]}, {k, 0, m}], PlotJoined\ -> \ False, \t
+ PlotRange -> {{\(-5\), 5}, {\(-4\), 4}}, \n\tPlotStyle -> Blue,
+ Prolog\ -> \ AbsolutePointSize[5], AspectRatio -> 0.5,
+ AxesLabel -> {"\<> x\>", "\< ^ y\>"}]\)], "Input"],
+
+Cell[BoxData[
+ \(linienplot =
+ ListPlot[Table[{xp[k], yp[k]}, {k, 0, m}], PlotJoined\ -> \ True, \t
+ PlotRange -> {{\(-5\), 5}, {\(-4\), 4}}, \n\tPlotStyle -> Blue,
+ Prolog\ -> \ AbsolutePointSize[5], AspectRatio -> 0.5,
+ AxesLabel -> {"\<> x\>", "\< ^ y\>"}]\)], "Input"],
+
+Cell[BoxData[
+ \(Show[ellipsplot, linienplot, punktplot,
+ Prolog\ -> \ AbsolutePointSize[5]]\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{" ",
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Newton\ - \
+ Interpolation\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
+\ \ \ \ *) \),
+ "Section",
+ FontColor->RGBColor[1, 0, 0]]}]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[
+ RowBox[{" ",
+ StyleBox[\( (*\ \ \ \ \ \ \ \ Funktionsunterprogramm\ zur\ Berechnung\ \
+der\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 1]], "\[IndentingNewLine]",
+ " ",
+ StyleBox[\( (*\ \ \ \ \ Dividierte\ Differenzen\ f\[UDoubleDot]r\ die\ \
+Newton - Interpolation\ \ \ \ \ \ \ \ \ \ \ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 1]], " "}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ \(FunkDivDiff[xpform_,
+ ypform_] := \ \((\[IndentingNewLine]Do[
+ DivDiffret[k,
+ 1] = \((ypform[k + 1] - ypform[k])\)/\((xpform[k + 1] -
+ xpform[k])\), {k, 0, m - 1}]; \[IndentingNewLine]Do[
+ Do[DivDiffret[k,
+ j] = \((DivDiffret[k + 1, j - 1] -
+ DivDiffret[k, j - 1])\)/\((xpform[k + j] -
+ xpform[k])\), {k, 0, m - j}], {j, 2, m}];
+ DivDiffmatret =
+ Table[DivDiffret[0, j], {j, 1, m}]; {DivDiffmatret})\)\)], "Input"],
+
+Cell[BoxData[
+ \(\(DivDiffxmat = FunkDivDiff[tp, xp]\ ;\)\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{\(DivDiffx = DivDiffxmat[\([1]\)];\),
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]]}]],
+ StyleBox[\( (*\ \ Dividierte\ Differenzen\ f\[UDoubleDot]r\ die\ x -
+ Werte\ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]]}]], "Input"],
+
+Cell[BoxData[
+ RowBox[{\(DivDiffymat = FunkDivDiff[tp, yp]\ ;\),
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]]}]], "Input"],
+
+Cell[BoxData[
+ RowBox[{\(DivDiffy = DivDiffymat[\([1]\)];\), " ",
+ StyleBox[\( (*\ \ Dividierte\ Differenzen\ f\[UDoubleDot]r\ die\ y -
+ Werte\ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]]}]], "Input"],
+
+Cell[BoxData[
+ RowBox[{" ",
+ StyleBox[\( (*\ \ \ \ St\[UDoubleDot]tzstellen\ xj\ und\ yj\ f\
+\[UDoubleDot]r\ den\ Graph\ der\ Newton - Interpolation\ \ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]]}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ \(Do[{xnew[j] = xp[0],
+ prox = tj[j] -
+ tp[0], \[IndentingNewLine]Do[{xnew[j] =
+ xnew[j] + prox*DivDiffx[\([i]\)],
+ prox = prox*\((tj[j] - tp[i])\)}, {i, 1,
+ m}], \[IndentingNewLine]ynew[j] = yp[0],
+ proy = tj[j] - tp[0], \n\t
+ Do[{ynew[j] = ynew[j] + proy*DivDiffy[\([i]\)],
+ proy = proy*\((tj[j] - tp[i])\)}, {i, 1, m}]}, {j, 0,
+ nd}]\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+ StyleBox[
+ RowBox[{" ",
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]]}]],
+ StyleBox[\( (*\ \ \ \ Parametrische\ Darstellung\ der\ Newton -
+ Interpolation\ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]]}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ \(newtonplot =
+ ListPlot[Table[{xnew[j], ynew[j]}, {j, 0, nd}],
+ PlotJoined\ -> \ True, \n\t
+ PlotRange -> {{\(-5\), 5}, {\(-4\), 4}}, \tPlotStyle -> Red,
+ AspectRatio -> 0.5, AxesLabel -> {"\<> x\>", "\< ^ y\>"}]\)], "Input"],
+
+Cell[BoxData[
+ \(\(\(Show[newtonplot, ellipsplot, linienplot, punktplot,
+ Prolog\ -> \ AbsolutePointSize[5]]\)\(\[IndentingNewLine]\)
+ \)\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{" ",
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ Nat\[UDoubleDot]rliche\ Spline -
+ Interpolation\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \
+\),
+ "Section",
+ FontColor->RGBColor[1, 0, 0]]}]], "Input",
+ Background->RGBColor[0, 1, 0]],
+
+Cell[BoxData[
+ RowBox[{" ",
+ StyleBox[\( (*\ \ \ \ \ \ \ \ Funktionsunterprogramm\ zur\ Berechnung\ \
+der\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 1]], "\[IndentingNewLine]",
+ " ",
+ StyleBox[\( (*\ \ \ \ \ Koeffizienten\ f\[UDoubleDot]r\ die\ nat\
+\[UDoubleDot]rlichen\ Spline - Interpolation\ \ \ \ \ \ \ \ \ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 1]], " "}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ RowBox[{\(FunkNatSpl[xpform_, ypform_]\), ":=", " ",
+ RowBox[{
+ "(", "\[IndentingNewLine]", " ",
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Erstellen\ \
+der\ Tridiagonalmatrix\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 1]], "\n",
+ " ",
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ \((\
+ Haupt - \ und\ Nebendiagonale\ )\)\ \ \ \ \ \ \ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]], "\[IndentingNewLine]",
+ RowBox[{\(Du[0] = xpform[1] - xpform[0]\), ";", "\n",
+ " ", \(Do[{Du[k] = xpform[k + 1] - xpform[k],
+ Dh[k] = 2 \((Du[k - 1] + Du[k])\)}, {k, 1, m - 1}]\), ";",
+ "\[IndentingNewLine]", " ",
+
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ Cholesky -
+ Zerlegung\ der\ Tridiagonalmatrix\ \ \ \ \ \ \ \ \ \ \ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 1]],
+ "\[IndentingNewLine]", \(Ch[1] = Sqrt[Dh[1]]\), ";", "\n",
+ " ", \(Do[{Cn[k - 1] = Du[k - 1]/Ch[k - 1],
+ Ch[k] = Sqrt[Dh[k] - Cn[k - 1]^2]}, {k, 2, m - 1}]\), ";",
+ "\[IndentingNewLine]", " ",
+
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ Vorw\[ADoubleDot]rtsrechnung\ \
+"\<von oben her\>"\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["\n",
+ FontColor->RGBColor[1, 0, 1]], " ",
+
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ und\ Erstellen\ der\ rechten\ \
+Seite\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]],
+ "\[IndentingNewLine]", \(Dv[0] = ypform[1] - ypform[0]\), ";",
+ " ", \(Dv[1] = ypform[2] - ypform[1]\), ";", "\n",
+ " ", \(Dr[1] = 3 \((Dv[1]/Du[1] - Dv[0]/Du[0])\)\), ";", "\n",
+ " ", \(Z[1] = Dr[1]/Ch[1]\), ";", "\n",
+ " ", \(Do[{Dv[k] = ypform[k + 1] - ypform[k], \n\t\tDr[k] =
+ 3 \((Dv[k]/Du[k] - Dv[k - 1]/Du[k - 1])\), \n\t\tZ[
+ k] = \((Dr[k] - Z[k - 1]*Cn[k - 1])\)/Ch[k]}, \n\ \ \ {k,
+ 2, m - 1}]\), ";", "\[IndentingNewLine]",
+ " ",
+
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ R\[UDoubleDot]ckw\
+\[ADoubleDot]rtsrechnung\ "\<von unten her\>"\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
+\ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["\n",
+ FontColor->RGBColor[1, 0, 1]], " ",
+
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ \tBerechnung\ der\ \
+Koeffizienten\ B\_k\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]],
+ "\[IndentingNewLine]", \(B[m] = 0\), ";",
+ " ", \(B[m - 1] = Z[m - 1]/Ch[m - 1]\), ";", "\n",
+ " ", \(Do[
+ B[k] = \((Z[k] - B[k + 1]*Cn[k])\)/Ch[k], {k, m - 2,
+ 1, \(-1\)}]\), ";", " ", \(B[0] = 0\), ";",
+ "\[IndentingNewLine]", " ",
+
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ \ Berechnung\ der\ \
+Koeffizienten\ A\_\(\(k\)\(\ \)\), \ C\_k\ , \
+ D\_k\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]],
+ "\[IndentingNewLine]", \(Do[{A[
+ k] = \((B[k + 1] - B[k])\)/\((3
+ Du[k])\), \n\t\t\ \ \ \ \ \ \ \ \ \ \ \ \ Cc[k] =
+ Dv[k]/Du[k] - Du[k]*\((B[k + 1] + 2 B[k])\)/3, \
+ Dc[k] = ypform[k]}, {k, 0, m - 1}]\), ";",
+ "\[IndentingNewLine]",
+ " ", \(Aret = Table[A[k], \ {k, 0, m - 1}]\), ";",
+ " ", \(Bret = Table[B[k], {k, 0, m}]\), ";", " ",
+ "\[IndentingNewLine]", " ", \(Cret = Table[Cc[k], {k, 0, m - 1}]\),
+ ";", " ", \(Dret = Table[Dc[k], {k, 0, m - 1}]\), ";",
+ "\[IndentingNewLine]", \({Aret, Bret, Cret, Dret}\)}],
+ ")"}]}]], "Input"],
+
+Cell[BoxData[
+ \(\(ABCDxmat = FunkNatSpl[tp, xp]\ \ ;\)\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{\(Anatx = ABCDxmat[\([1]\)]\ ;\), " ",
+ StyleBox[\( (*\
+ Koeffizienen\ Ak\ \ \(f \[UDoubleDot]r\)\ die\ x - Werte\ *) \),
+ FontColor->RGBColor[1, 0, 1],
+ Background->None]}]], "Input"],
+
+Cell[BoxData[
+ RowBox[{\(Bnatx = ABCDxmat[\([2]\)];\), " ",
+ RowBox[{
+ StyleBox["(*",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ RowBox[{
+ RowBox[{
+ StyleBox["Koeffizienen",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["Bk",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[\(f \[UDoubleDot]r\),
+ FontColor->RGBColor[1, 0, 1],
+ Background->None],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1],
+ Background->None],
+ StyleBox["die",
+ FontColor->RGBColor[1, 0, 1],
+ Background->None],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1],
+ Background->None],
+ StyleBox["x",
+ FontColor->RGBColor[1, 0, 1],
+ Background->None]}],
+ StyleBox["-",
+ FontColor->RGBColor[1, 0, 1],
+ Background->None],
+ StyleBox["Werte",
+ FontColor->RGBColor[1, 0, 1],
+ Background->None]}],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["*)",
+ FontColor->RGBColor[1, 0, 1]]}]}]], "Input"],
+
+Cell[BoxData[
+ RowBox[{\(Cnatx = ABCDxmat[\([3]\)];\), " ",
+ RowBox[{
+ StyleBox["(*",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ RowBox[{
+ RowBox[{
+ StyleBox["Koeffizienen",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["Ck",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[\(f \[UDoubleDot]r\),
+ FontColor->RGBColor[1, 0, 1],
+ Background->None],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1],
+ Background->None],
+ StyleBox["die",
+ FontColor->RGBColor[1, 0, 1],
+ Background->None],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1],
+ Background->None],
+ StyleBox["x",
+ FontColor->RGBColor[1, 0, 1],
+ Background->None]}],
+ StyleBox["-",
+ FontColor->RGBColor[1, 0, 1],
+ Background->None],
+ StyleBox["Werte",
+ FontColor->RGBColor[1, 0, 1],
+ Background->None]}],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["*)",
+ FontColor->RGBColor[1, 0, 1]]}]}]], "Input"],
+
+Cell[BoxData[
+ RowBox[{\(Dnatx = ABCDxmat[\([4]\)];\), " ",
+ RowBox[{
+ StyleBox["(*",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ RowBox[{
+ RowBox[{
+ StyleBox["Koeffizienen",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["Dk",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[\(f \[UDoubleDot]r\),
+ FontColor->RGBColor[1, 0, 1],
+ Background->None],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1],
+ Background->None],
+ StyleBox["die",
+ FontColor->RGBColor[1, 0, 1],
+ Background->None],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1],
+ Background->None],
+ StyleBox["x",
+ FontColor->RGBColor[1, 0, 1],
+ Background->None]}],
+ StyleBox["-",
+ FontColor->RGBColor[1, 0, 1],
+ Background->None],
+ StyleBox["Werte",
+ FontColor->RGBColor[1, 0, 1],
+ Background->None]}],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["*)",
+ FontColor->RGBColor[1, 0, 1]]}]}]], "Input"],
+
+Cell[BoxData[
+ \(\(ABCDymat = FunkNatSpl[tp, yp]\ ;\)\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{\(Anaty = ABCDymat[\([1]\)];\), " ",
+ StyleBox[\( (*\
+ Koeffizienen\ Ak\ \ \(f \[UDoubleDot]r\)\ die\ x - Werte\ *) \),
+ FontColor->RGBColor[1, 0, 1],
+ Background->None]}]], "Input"],
+
+Cell[BoxData[
+ RowBox[{\(Bnaty = ABCDymat[\([2]\)];\), " ",
+ RowBox[{
+ StyleBox["(*",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ RowBox[{
+ RowBox[{
+ StyleBox["Koeffizienen",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["Bk",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[\(f \[UDoubleDot]r\),
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