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Difference between revisions 54065347 and 54065513 on enwiki(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.2' 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: [email protected] phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*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, hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1, phixy, 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], 1000, \[IndentingNewLine]\[IndentingNewLine]D[ Gfun[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy, hxyp1, hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1, phixy, phixyp1, phixp1y], phixyp1], 1000, D[Gfun[hxm2y, hxm1ym1, hxm1y, hxm1yp1, hxym2, hxym1, hxy, hxyp1, hxyp2, hxp1ym1, hxp1y, hxp1yp1, hxp2y, phixm1y, phixym1, phixy, phixyp1, phixp1y], phixp1y], 1000}]]\)\(\n\)\(\n\) \)\)], "Input"], Cell[BoxData[{ \(L[x_, \ y_] = D[D[h[x, \ y], \ x], \ x] + D[D[h[x, \ y], \ y], \ y]; Lx[x_, \ y_] = D[L[x, \ y], \ x]; Ly[x_, \ y_] = D[L[x, \ y], \ y];\), "\[IndentingNewLine]", \(\(FCont[x_, \ y_] = \[IndentingNewLine]h[x, \ y] + cfl*\((D[a[phi[x, \ y]]*H3[h[x, \ y]]*Lx[x, \ y], \ x] + D[a[phi[x, \ y]]*H3[h[x, \ y]]*Ly[x, \ y], \ y])\) + cfl*gridsize^3* D[b[phi[x, \ y]]*H3[h[x, \ y]] + C1*phi[x, \ y]*h[x, \ y]*f[phi[x, \ y]]*w[h[x, \ y]], \ x] - cfl*Dinclination* gridsize^2*\((D[ a[phi[x, y]]*\((H3[h[x, y]]* D[rho[phi[x, y]]*h[x, y], x] - \((5/8)\)* H4[h[x, y]]*D[rho[phi[x, y]], x])\), x] + D[a[phi[x, y]]*\((H3[h[x, y]]* D[rho[phi[x, y]]*h[x, y], y] - \((5/8)\)* H4[h[x, y]]*D[rho[phi[x, y]], y])\), y])\);\)\), "\[IndentingNewLine]", \(\(GCont[x_, \ y_] = \[IndentingNewLine]h[x, \ y]*phi[x, \ y] + cfl*\((D[c[phi[x, \ y]]*H3[h[x, \ y]]*Lx[x, \ y], \ x] + D[c[phi[x, \ y]]*H3[h[x, \ y]]*Ly[x, \ y], \ y])\) + cfl*gridsize^3* D[d[phi[x, \ y]]*H3[h[x, \ y]] + C2*phi[x, \ y]*h[x, \ y]*f[phi[x, \ y]]*w[h[x, \ y]], \ x] - cfl*Dinclination* gridsize^2*\((D[ c[phi[x, y]]*\((H3[h[x, y]]* D[rho[phi[x, y]]*h[x, y], x] - \((5/8)\)* H4[h[x, y]]*D[rho[phi[x, y]], x])\), x] + D[c[phi[x, y]]*\((H3[h[x, y]]* D[rho[phi[x, y]]*h[x, y], y] - \((5/8)\)* H4[h[x, y]]*D[rho[phi[x, y]], y])\), y])\);\)\), "\[IndentingNewLine]", \(\)}], "Input"], Cell[BoxData[{ \(\(hxy = h[x, y];\)\), "\n", \(\(hxp1y = h[x + alpha, y];\)\), "\n", \(\(hxp2y = h[x + 2*alpha, y];\)\), "\n", \(\(hxm1y = h[x - alpha, y];\)\), "\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", \(\(phixm1y = phi[x - alpha, y];\)\), "\n", \(\(phixyp1 = phi[x, y + beta];\)\), "\n", \(\(phixym1 = phi[x, y - beta];\)\), "\[IndentingNewLine]", \(\)}], "Input"], 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"] }, FrontEndVersion->"5.2 for X", ScreenRectangle->{{0, 1280}, {0, 1024}}, WindowSize->{1139, 993}, WindowMargins->{{0, Automatic}, {Automatic, 0}} ] (******************************************************************* 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[1754, 51, 1010, 17, 155, "Input"], Cell[2767, 70, 3156, 53, 315, "Input"], Cell[5926, 125, 2186, 35, 203, "Input"], Cell[8115, 162, 918, 16, 107, "Input"], Cell[9036, 180, 661, 11, 107, "Input"], Cell[9700, 193, 1378, 22, 219, "Input"], Cell[11081, 217, 2546, 43, 251, "Input"], Cell[13630, 262, 7887, 118, 1003, "Input"], Cell[21520, 382, 1967, 38, 235, "Input"], Cell[23490, 422, 900, 19, 315, "Input"], Cell[24393, 443, 351, 6, 75, "Input"], Cell[24747, 451, 322, 6, 75, "Input"], Cell[25072, 459, 26, 0, 27, "Input"], Cell[25101, 461, 74, 1, 27, "Input"], Cell[25178, 464, 74, 1, 27, "Input"] } ] *) (******************************************************************* End of Mathematica Notebook file. *******************************************************************)# Abel's integral -------- Abelian integral # Mathematical abstraction -------- Abstraction (mathematics) # Anosov map -------- Anosov automorphism # Archimedean bodies -------- Archimedean solids # Birth-and-death process -------- Birth-death process # Characteristic mapping -------- Characteristic map # Adjoint representation of a Lie group -------- Adjoint representation # Asymptotic expression -------- Asymptotic expansion # Cadlag function -------- Cadlag # Cadlag functions -------- Cadlag # Centered polygonal number -------- Centered number # Characteristic mapping -------- Characteristic map # Chinese theorem -------- Chinese remainder theorem # Circuminscribed -------- Circumscribe # Complete beta function -------- Beta function # Congruence in geometry -------- Congruence (geometry) # Connected surface -------- Connected space # Convolution of functions -------- Convolution # Conway game -------- Conway's Game of Life # Curve of constant breadth -------- Curve of constant width # Diffie-Hellman protocol -------- Diffie-Hellman problem # Disconnected space -------- Disconnected set # Dispersion equation -------- Dispersion relation # Eisenstein unit -------- Einstein (unit) # Enantiomorphous -------- Enantiomorphic # Enumerable -------- Enumerate # Erdos-Turán conjecture -------- Erdős-Turan conjecture # Essential singular point -------- Essential singularity # Euler's totient rule -------- Euler's totient theorem # Euler-Maclaurin sum formula -------- Euler-Maclaurin formula # Eulerian number -------- Euler number # Evolution strategies -------- Evolution strategy 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?diff=prev&oldid=54065513.
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