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Prolog\ -> \ AbsolutePointSize[5], AspectRatio -> 0.5, AxesLabel -> {"\<> x\>", "\< ^ y\>"}]\)], "Input"], Cell[BoxData[ \(Show[achtplot, linienplot, punktplot, Prolog\ -> \ AbsolutePointSize[5]]\)], "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] = 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AspectRatio -> 0.5, AxesLabel -> {"\<> x\>", "\< ^ y\>"}]\)], "Input"], Cell[BoxData[ \(\(\(Show[achtplot, newtonplot, linienplot, punktplot, Prolog\ -> \ AbsolutePointSize[5]]\)\(\[IndentingNewLine]\) \)\)], "Input"], Cell[BoxData[ RowBox[{" ", StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ Periodische\ Spline - Interpolation\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \ \), "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\ \ periodischen\ Spline - Interpolation\ \ \ \ \ \ \ \ \ *) \), "Subsubtitle", FontColor->RGBColor[1, 0, 1]], " "}]], "Input", Background->RGBColor[1, 1, 0]], Cell[BoxData[ RowBox[{\(FunkPerSpl[xpform_, ypform_]\), ":=", " ", RowBox[{ "(", 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Sqrt[Dh[0]]\), ";", " ", \(Cp[0] = Du[m - 1]/Ch[0]\), ";", "\n", " ", \(Do[{Cn[k - 1] = Du[k - 1]/Ch[k - 1], Ch[k] = Sqrt[Dh[k] - Cn[k - 1]^2], \ \ \ Cp[ k] = \((\ Dp[k] - Cp[k - 1]*Cn[k - 1]\ )\)/Ch[k]}, {k, 1, m - 2}]\), ";", "\[IndentingNewLine]", " ", \(Csum = 0\), ";", " ", \(Do[\ Csum = Csum + Cp[i]^2, {i, 1, m - 2}]\), ";", "\[IndentingNewLine]", " ", \(Cn[m - 2] = Cp[m - 2]\), ";", " ", \(Ch[m - 1] = Sqrt[\ Dh[m - 1] - Csum]\), ";", "\[IndentingNewLine]", " ", StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ Vorw\[ADoubleDot]rtsrechnung\ \ "\"\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \), FontColor->RGBColor[1, 0, 1]], StyleBox["\n", FontColor->RGBColor[1, 0, 1]], " ", StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ und\ Erstellen\ der\ rechten\ \ Seite\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \), FontColor->RGBColor[1, 0, 1]], "\[IndentingNewLine]", \(Dv[0] = ypform[1] - ypform[0]\), ";", " ", \(Dv[m - 1] = ypform[m] - ypform[m - 1]\), ";", "\n", " ", \(Dr[0] = 3 \((Dv[0]/Du[0] - Dv[m - 1]/Du[m - 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= \((\ Z[k] - B[k + 1]*Cn[k] - Cp[k]*B[m - 1])\)/Ch[k], {k, m - 2, 0, \(-1\)}]\), ";", "\[IndentingNewLine]", " ", \(B[m] = B[0]\), ";", "\[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[ RowBox[{ RowBox[{\(ABCDxmat = FunkPerSpl[tp, xp]\ \ ;\), "\n", RowBox[{\(Aperx = ABCDxmat[\([1]\)]\ ;\), " ", 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