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Revision 54065347 of "User:Mathbot/Page33" on enwiki(************** Content-type: application/mathematica **************
CreatedBy='Mathematica 5.2'
Mathematica-Compatible Notebook
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*******************************************************************)
(*CacheID: 232*)
(*NotebookFileLineBreakTest
NotebookFileLineBreakTest*)
(*NotebookOptionsPosition[ 25256, 467]*)
(*NotebookOutlinePosition[ 25885, 489]*)
(* CellTagsIndexPosition[ 25841, 485]*)
(*WindowFrame->Normal*)
Notebook[{
Cell[BoxData[
\(\(\(phixp15y = \((phixy + phixp1y)\)/2; \ \ hxp15y = \((hxy + hxp1y)\)/
2; Qxpy = H3[hxp15y]*a[phixp15y]; \ Rxpy = H3[hxp15y]*c[phixp15y];\ \n
phixm15y = \((phixy + phixm1y)\)/2; \ \ hxm15y = \((hxy + hxm1y)\)/2;
Qxmy = H3[hxm15y]*a[phixm15y]; \ Rxmy = H3[hxm15y]*c[phixm15y];\n
phixyp15 = \((phixy + phixyp1)\)/2; \ \ \ hxyp15 = \((hxy + hxyp1)\)/2; \
Qxyp = H3[hxyp15]*a[phixyp15]; \ \ Rxyp = H3[hxyp15]*c[phixyp15];\n
phixym15 = \((phixy + phixym1)\)/2; \ \ \ hxym15 = \((hxy + hxym1)\)/2; \
Qxym = H3[hxym15]*a[phixym15]; \ \ Rxym =
H3[hxym15]*c[phixym15];\[IndentingNewLine]
psixp15y = \((phixy*hxy + phixp1y*hxp1y)\)/2;
psixm15y = \((phixy*hxy + phixm1y*hxm1y)\)/2;\[IndentingNewLine]
\(rhoxy = rho[phixy];\)\ \[IndentingNewLine]
rhoxp1y = rho[phixp1y]; rhoxm1y = rho[phixm1y];\ \[IndentingNewLine]
\(\(rhoxyp1 = rho[phixyp1]; \ \ rhoxym1 =
rho[phixym1];\)\(\[IndentingNewLine]\)
\)\)\(\ \)\)\)], "Input"],
Cell[BoxData[{
\(\(\(FfunNoDpart[hxm2y_, hxm1ym1_, hxm1y_, hxm1yp1_, hxym2_, hxym1_,
hxy_, hxyp1_, hxyp2_, hxp1ym1_, hxp1y_, hxp1yp1_, hxp2y_, phixm1y_,
phixym1_, phixy_, phixyp1_,
phixp1y_] = \((\((\(-\((\((\((\(-3\)*hxy - hxym2 + 3*hxym1 +
hxyp1)\)/
Power[beta,
3] + \((\(-2\)*hxy + hxm1y +
hxp1y)\)/\((Power[alpha, 2]*
beta)\) - \((\(-2\)*hxym1 + hxm1ym1 +
hxp1ym1)\)/\((Power[alpha, 2]*beta)\))\)*
Qxym)\)\) + \((\((3*hxy - hxym1 - 3*hxyp1 +
hxyp2)\)/
Power[beta,
3] - \((\(-2\)*hxy + hxm1y +
hxp1y)\)/\((Power[alpha, 2]*
beta)\) + \((\(-2\)*hxyp1 + hxm1yp1 +
hxp1yp1)\)/\((Power[alpha, 2]*beta)\))\)*
Qxyp)\)/
beta + \((\(-\((\((\((\(-2\)*hxy + hxym1 + hxyp1)\)/\((alpha*
Power[beta, 2])\) - \((\(-2\)*hxm1y +
hxm1ym1 + hxm1yp1)\)/\((alpha*
Power[beta, 2])\) + \((\(-3\)*hxy -
hxm2y + 3*hxm1y + hxp1y)\)/
Power[alpha, 3])\)*
Qxmy)\)\) + \((\(-\((\((\(-2\)*hxy + hxym1 +
hxyp1)\)/\((alpha*
Power[beta, 2])\))\)\) + \((\(-2\)*
hxp1y + hxp1ym1 + hxp1yp1)\)/\((alpha*
Power[beta, 2])\) + \((3*hxy - hxm1y -
3*hxp1y + hxp2y)\)/Power[alpha, 3])\)*Qxpy)\)/
alpha)\) +
gridsize^3*\((b[phixp15y]*H3[hxp15y] +
C1*psixp15y*f[phixp15y]*w[hxp15y] -
b[phixm15y]*H3[hxm15y] -
C1*psixm15y*f[phixm15y]*w[hxm15y])\)/
alpha;\)\(\[IndentingNewLine]\)
\)\), "\[IndentingNewLine]",
\(\(FfunDpart[hxm2y_, hxm1ym1_, hxm1y_, hxm1yp1_, hxym2_, hxym1_, hxy_,
hxyp1_, hxyp2_, hxp1ym1_, hxp1y_, hxp1yp1_, hxp2y_, phixm1y_,
phixym1_, phixy_, phixyp1_, phixp1y_] =
gridsize^2*\((Qxpy*\((hxp1y*rhoxp1y - hxy*rhoxy)\) -
Qxmy*\((hxy*rhoxy - hxm1y*rhoxm1y)\))\)/
Power[alpha, 2] - \((5/8)\)*
gridsize^2*\((H4[hxp15y]*a[phixp15y]*\((rhoxp1y - rhoxy)\) -
H4[hxm15y]*a[phixm15y]*\((rhoxy - rhoxm1y)\))\)/
Power[alpha, 2] +
gridsize^2*\((Qxyp*\((hxyp1*rhoxyp1 - hxy*rhoxy)\) -
Qxym*\((hxy*rhoxy - hxym1*rhoxym1)\))\)/
Power[beta, 2] - \((5/8)\)*
gridsize^2*\((H4[hxyp15]*a[phixyp15]*\((rhoxyp1 - rhoxy)\) -
H4[hxym15]*a[phixym15]*\((rhoxy - rhoxym1)\))\)/
Power[beta, 2];\)\), "\n",
\(\)}], "Input"],
Cell[BoxData[
\(\(GfunNoDpart[hxm2y_, hxm1ym1_, hxm1y_, hxm1yp1_, hxym2_, hxym1_, hxy_,
hxyp1_, hxyp2_, hxp1ym1_, hxp1y_, hxp1yp1_, hxp2y_, phixm1y_,
phixym1_, phixy_, phixyp1_,
phixp1y_] = \((\((\(-\((\((\((\(-3\)*hxy - hxym2 + 3*hxym1 +
hxyp1)\)/
Power[beta,
3] + \((\(-2\)*hxy + hxm1y +
hxp1y)\)/\((Power[alpha, 2]*
beta)\) - \((\(-2\)*hxym1 + hxm1ym1 +
hxp1ym1)\)/\((Power[alpha, 2]*beta)\))\)*
Rxym)\)\) + \((\((3*hxy - hxym1 - 3*hxyp1 +
hxyp2)\)/
Power[beta,
3] - \((\(-2\)*hxy + hxm1y +
hxp1y)\)/\((Power[alpha, 2]*
beta)\) + \((\(-2\)*hxyp1 + hxm1yp1 +
hxp1yp1)\)/\((Power[alpha, 2]*beta)\))\)*
Rxyp)\)/
beta + \((\(-\((\((\((\(-2\)*hxy + hxym1 + hxyp1)\)/\((alpha*
Power[beta, 2])\) - \((\(-2\)*hxm1y +
hxm1ym1 + hxm1yp1)\)/\((alpha*
Power[beta, 2])\) + \((\(-3\)*hxy -
hxm2y + 3*hxm1y + hxp1y)\)/
Power[alpha, 3])\)*
Rxmy)\)\) + \((\(-\((\((\(-2\)*hxy + hxym1 +
hxyp1)\)/\((alpha*
Power[beta, 2])\))\)\) + \((\(-2\)*
hxp1y + hxp1ym1 + hxp1yp1)\)/\((alpha*
Power[beta, 2])\) + \((3*hxy - hxm1y -
3*hxp1y + hxp2y)\)/Power[alpha, 3])\)*Rxpy)\)/
alpha)\) +
gridsize^3*\((d[phixp15y]*H3[hxp15y] +
C2*psixp15y*f[phixp15y]*w[hxp15y] -
d[phixm15y]*H3[hxm15y] -
C2*psixm15y*f[phixm15y]*w[hxm15y])\)/alpha;\)\)], "Input"],
Cell[BoxData[
\(\(\(GfunDpart[hxm2y_, hxm1ym1_, hxm1y_, hxm1yp1_, hxym2_, hxym1_, hxy_,
hxyp1_, hxyp2_, hxp1ym1_, hxp1y_, hxp1yp1_, hxp2y_, phixm1y_,
phixym1_, phixy_, phixyp1_, phixp1y_] =
gridsize^2*\((Rxpy*\((hxp1y*rhoxp1y - hxy*rhoxy)\) -
Rxmy*\((hxy*rhoxy - hxm1y*rhoxm1y)\))\)/
Power[alpha, 2] - \((5/8)\)*
gridsize^2*\((H4[hxp15y]*c[phixp15y]*\((rhoxp1y - rhoxy)\) -
H4[hxm15y]*c[phixm15y]*\((rhoxy - rhoxm1y)\))\)/
Power[alpha, 2] +
gridsize^2*\((Rxyp*\((hxyp1*rhoxyp1 - hxy*rhoxy)\) -
Rxym*\((hxy*rhoxy - hxym1*rhoxym1)\))\)/
Power[beta, 2] - \((5/8)\)*
gridsize^2*\((H4[hxyp15]*c[phixyp15]*\((rhoxyp1 - rhoxy)\) -
H4[hxym15]*c[phixym15]*\((rhoxy - rhoxym1)\))\)/
Power[beta, 2];\)\(\n\)
\)\)], "Input"],
Cell[BoxData[
\(\(Ffun[hxm2y_, hxm1ym1_, hxm1y_, hxm1yp1_, hxym2_, hxym1_, hxy_,
hxyp1_, hxyp2_, hxp1ym1_, hxp1y_, hxp1yp1_, hxp2y_, phixm1y_,
phixym1_, phixy_, phixyp1_, phixp1y_] =
hxy + cfl*
FfunNoDpart[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy,
hxyp1, hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1,
phixy, phixyp1, phixp1y] -
cfl*Dinclination*
FfunDpart[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy,
hxyp1, hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1,
phixy, phixyp1, phixp1y];\)\)], "Input"],
Cell[BoxData[{
\(\(GfunUntweaked[hxm2y_, hxm1ym1_, hxm1y_, hxm1yp1_, hxym2_, hxym1_,
hxy_, hxyp1_, hxyp2_, hxp1ym1_, hxp1y_, hxp1yp1_, hxp2y_, phixm1y_,
phixym1_, phixy_, phixyp1_, phixp1y_] =
phixy*hxy +
cfl*GfunNoDpart[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy,
hxyp1, hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1,
phixy, phixyp1, phixp1y] -
cfl*Dinclination*
GfunDpart[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy,
hxyp1, hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1,
phixy, phixyp1, phixp1y];\)\), "\[IndentingNewLine]",
\(\(Gfun[hxm2y_, hxm1ym1_, hxm1y_, hxm1yp1_, hxym2_, hxym1_, hxy_,
hxyp1_, hxyp2_, hxp1ym1_, hxp1y_, hxp1yp1_, hxp2y_, phixm1y_,
phixym1_, phixy_, phixyp1_, phixp1y_] =
Simplify[
phixy + \((GfunUntweaked[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2,
hxym1, hxy, hxyp1, hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y,
phixm1y, phixym1, phixy, phixyp1, phixp1y] -
phixy*Ffun[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1,
hxy, hxyp1, hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y,
phixm1y, phixym1, phixy, phixyp1, phixp1y])\)/
hxy];\)\)}], "Input"],
Cell[BoxData[
\(\(\( (*\(\(**\)\(\(*\)\(\ \)\(This\)\(\ \)\(is\)\(\ \)\(Gfun\)\(\ \
\)\(simplified\)\)\), \ using\ the\ fact\ that\ c[phi] = phi*a[phi], \
d[phi] = phi*b[phi]\ *****) \)\(\[IndentingNewLine]\)\(GfunS[hxm2y_,
hxm1ym1_, hxm1y_, hxm1yp1_, hxym2_, hxym1_, hxy_, hxyp1_, hxyp2_,
hxp1ym1_, hxp1y_, hxp1yp1_, hxp2y_, phixm1y_, phixym1_, phixy_,
phixyp1_, phixp1y_] =
phixy + cfl*\((\((an[phixy]*
H3[hxy]*\((\((hxp2y - 2*hxp1y + 2*hxm1y -
hxm2y)\)/\((2*alpha^3)\) + \((hxp1yp1 -
2*hxp1y + hxp1ym1 - hxm1yp1 + 2*hxm1y -
hxm1ym1)\)/\((2*alpha*
beta^2)\))\)*\((phixp1y - phixm1y)\)/\((2*
alpha)\) +
an[phixy]*
H3[hxy]*\((\((hxyp2 - 2*hxyp1 + 2*hxym1 -
hxym2)\)/\((2*beta^3)\) + \((hxp1yp1 -
2*hxyp1 + hxm1yp1 - hxp1ym1 + 2*hxym1 -
hxm1ym1)\)/\((2*alpha^2*
beta)\))\)*\((phixyp1 - phixym1)\)/\((2*
beta)\))\)/hxy +
gridsize^3*H3[hxy]*
bn[phixy]*\(\((phixp1y - phixm1y)\)/\((2*alpha)\)\)/hxy +
gridsize^3*\((C2 -
C1*phixy)\)*\(\((w[hxp1y]*f[phixp1y]*phixp1y*hxp1y -
w[hxm1y]*f[phixm1y]*phixm1y*hxm1y)\)/\((2*
alpha)\)\)/hxy -
Dinclination*gridsize^2*
an[phixy]*\((H3[
hxy]*\((phixp1y -
phixm1y)\)*\((rho[phixp1y]*hxp1y -
rho[phixm1y]*hxm1y)\)/\((4*alpha^2)\) - \((5/
8)\)*H4[
hxy]*\((phixp1y -
phixm1y)\)*\((rho[phixp1y] -
rho[phixm1y])\)/\((4*alpha^2)\) +
H3[hxy]*\((phixyp1 -
phixym1)\)*\((rho[phixyp1]*hxyp1 -
rho[phixym1]*hxym1)\)/\((4*beta^2)\) - \((5/
8)\)*H4[
hxy]*\((phixyp1 -
phixym1)\)*\((rho[phixyp1] -
rho[phixym1])\)/\((4*beta^2)\))\)/
hxy)\);\)\)\)], "Input"],
Cell[BoxData[
\(\(\(CForm[
Simplify[{Ffun[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy,
hxyp1, hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1,
phixy, phixyp1, phixp1y], 1000,
Gfun[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy, hxyp1,
hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1, phixy,
phixyp1, phixp1y], 1000,
D[Ffun[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy, hxyp1,
hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1, phixy,
phixyp1, phixp1y], hxm2y], 1000,
D[Ffun[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy, hxyp1,
hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1, phixy,
phixyp1, phixp1y], hxm1ym1], 1000,
D[Ffun[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy, hxyp1,
hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1, phixy,
phixyp1, phixp1y], hxm1y], 1000,
D[Ffun[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy, hxyp1,
hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1, phixy,
phixyp1, phixp1y], hxm1yp1], 1000,
D[Ffun[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy, hxyp1,
hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1, phixy,
phixyp1, phixp1y], hxym2], 1000,
D[Ffun[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy, hxyp1,
hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1, phixy,
phixyp1, phixp1y], hxym1], 1000,
D[Ffun[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy, hxyp1,
hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1, phixy,
phixyp1, phixp1y], hxy], 1000,
D[Ffun[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy, hxyp1,
hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1, phixy,
phixyp1, phixp1y], hxyp1], 1000,
D[Ffun[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy, hxyp1,
hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1, phixy,
phixyp1, phixp1y], hxyp2], 1000,
D[Ffun[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy, hxyp1,
hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1, phixy,
phixyp1, phixp1y], hxp1ym1], 1000,
D[Ffun[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy, hxyp1,
hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1, phixy,
phixyp1, phixp1y], hxp1y], 1000,
D[Ffun[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy, hxyp1,
hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1, phixy,
phixyp1, phixp1y], hxp1yp1], 1000,
D[Ffun[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy, hxyp1,
hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1, phixy,
phixyp1, phixp1y], hxp2y], 1000,
D[Ffun[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy, hxyp1,
hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1, phixy,
phixyp1, phixp1y], phixm1y], 1000,
D[Ffun[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy, hxyp1,
hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1, phixy,
phixyp1, phixp1y], phixym1], 1000,
D[Ffun[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy, hxyp1,
hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1, phixy,
phixyp1, phixp1y], phixy], 1000,
D[Ffun[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy, hxyp1,
hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1, phixy,
phixyp1, phixp1y], phixyp1], 1000,
D[Ffun[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy, hxyp1,
hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1, phixy,
phixyp1, phixp1y], phixp1y], 1000,
D[Gfun[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy, hxyp1,
hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1, phixy,
phixyp1, phixp1y], hxm2y], 1000,
D[Gfun[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy, hxyp1,
hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1, phixy,
phixyp1, phixp1y], hxm1ym1], 1000,
D[Gfun[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy, hxyp1,
hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1, phixy,
phixyp1, phixp1y], hxm1y], 1000,
D[Gfun[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy, hxyp1,
hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1, phixy,
phixyp1, phixp1y], hxm1yp1], 1000,
D[Gfun[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy, hxyp1,
hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1, phixy,
phixyp1, phixp1y], hxym2], 1000,
D[Gfun[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy, hxyp1,
hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1, phixy,
phixyp1, phixp1y], hxym1], 1000,
D[Gfun[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy, hxyp1,
hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1, phixy,
phixyp1, phixp1y], hxy], 1000,
D[Gfun[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy, hxyp1,
hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1, phixy,
phixyp1, phixp1y], hxyp1], 1000,
D[Gfun[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy, hxyp1,
hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1, phixy,
phixyp1, phixp1y], hxyp2], 1000,
D[Gfun[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy, hxyp1,
hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1, phixy,
phixyp1, phixp1y], hxp1ym1], 1000,
D[Gfun[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy, hxyp1,
hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1, phixy,
phixyp1, phixp1y], hxp1y], 1000,
D[Gfun[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy, hxyp1,
hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1, phixy,
phixyp1, phixp1y], hxp1yp1], 1000,
D[Gfun[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy, hxyp1,
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phixyp1, phixp1y], hxp2y], 1000,
D[Gfun[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy, hxyp1,
hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1, phixy,
phixyp1, phixp1y], phixm1y],
1000, \[IndentingNewLine]\[IndentingNewLine]D[
Gfun[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy, hxyp1,
hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1, phixy,
phixyp1, phixp1y], phixym1], 1000,
D[Gfun[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy, hxyp1,
hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1, phixy,
phixyp1, phixp1y], phixy],
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hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1, phixy,
phixyp1, phixp1y], phixp1y], 1000}]]\)\(\n\)\(\n\)
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\(\(FCont[x_, \ y_] = \[IndentingNewLine]h[x, \ y] +
cfl*\((D[a[phi[x, \ y]]*H3[h[x, \ y]]*Lx[x, \ y], \ x] +
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cfl*gridsize^3*
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\(\(GCont[x_, \ y_] = \[IndentingNewLine]h[x, \ y]*phi[x, \ y] +
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D[d[phi[x, \ y]]*H3[h[x, \ y]] +
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c[phi[x,
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D[rho[phi[x, y]]*h[x, y], x] - \((5/8)\)*
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\(\(hxp1y = h[x + alpha, y];\)\), "\n",
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\(\(hxm1y = h[x - alpha, y];\)\), "\n",
\(\(hxm2y = h[x - 2*alpha, y];\)\), "\n",
\(\(hxyp1 = h[x, y + beta];\)\), "\n",
\(\(hxyp2 = h[x, y + 2*beta];\)\), "\n",
\(\(hxym1 = h[x, y - beta];\)\), "\n",
\(\(hxym2 = h[x, y - 2*beta];\)\), "\n",
\(\(hxp1yp1 = h[x + alpha, y + beta];\)\), "\n",
\(\(hxp1ym1 = h[x + alpha, y - beta];\)\), "\n",
\(\(hxm1yp1 = h[x - alpha, y + beta];\)\), "\n",
\(\(hxm1ym1 = h[x - alpha, y - beta];\)\), "\n",
\(\(phixy = phi[x, y];\)\), "\n",
\(\(phixp1y = phi[x + alpha, y];\)\), "\n",
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\(\(phixyp1 = phi[x, y + beta];\)\), "\n",
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Cell[BoxData[
\(FSeries[x_, y_] =
Simplify[\[IndentingNewLine]\[IndentingNewLine]Normal[
Series[Ffun[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy,
hxyp1, hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1,
phixy, phixyp1, phixp1y], {alpha, 0, 0}, {beta, 0,
0}]]]\)], "Input"],
Cell[BoxData[
\(GSeries[x_, y_] =
Simplify[Normal[
Series[GfunUntweaked[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1,
hxy, hxyp1, hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y,
phixym1, phixy, phixyp1, phixp1y], {alpha, 0, 0}, {beta, 0,
0}]]]\)], "Input"],
Cell[BoxData[""], "Input"],
Cell[BoxData[
\(Simplify[FCont[x, \ y] - FSeries[x, \ y]]\)], "Input"],
Cell[BoxData[
\(Simplify[GCont[x, \ y] - GSeries[x, \ y]]\)], "Input"]
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*)
(*******************************************************************
End of Mathematica Notebook file.
*******************************************************************)All content in the above text box is licensed under the Creative Commons Attribution-ShareAlike license Version 4 and was originally sourced from https://en.wikipedia.org/w/index.php?oldid=54065347.
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