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                    Mathematica-Compatible Notebook

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Notebook[{

Cell[CellGroupData[{
Cell[BoxData[{
    \(\t\t\tClear[g, x, Ttotal, r, \[Alpha], \[Sigma], \[Theta]]\n\), 
    \(g[x_] = \ Max[Exp[x] - 1, 0]; \n\ r = 0.1; \[Sigma] = 0.25; 
    \[Alpha] = 2  r/\[Sigma]^2; \[Theta] = 0.35; \n
    Ttotal = Table[10. /3^\((16 - k)\), {k, 0, 16}]\), 
    \(Clear[x1, x2, x3]\), 
    \(\tinterpo[x1_, x2_, x3_] = 
      x3 - \((x3 - x2)\)^2/\((x1 - 2\ x2\  + x3)\); \n\n\t\t\n\t
    Clear[m, n, dt, dx, k, j, u, v, \[Lambda], s, SS]\), 
    \(\tmxMax\t = 6; \nmx = \((\(-1\))\); \n
    While[\((mx = mx + 1)\) < mxMax, \n
      \ {\ n = \ 12*2^mx + 4, \n\ \ 
        Print["\<Number of division = \>", n - 4], \n\ \ \ \ \ \ \ \ \ \ \ \t
        Print["\<====================================\>"], \n
        \ \ \ \ \ \ \ \ \ \t\tmt = 0, \ ST[mx] = {}, ST1[mx] = {}, \n\t\t
        While[\((mt = mt + 1)\) < Length[Ttotal] + 1, \ \n
          \t\t{\ \ dt = Ttotal[\([mt]\)]*\(\[Sigma]^2/2\)/\((n - 4)\), 
            \ \ \ \ dx = Sqrt[dt/\[Theta]], \n\ \ \ \ \ \ \ 
            Print["\< Calculating For T_max= \>", \ Ttotal[\([mt]\)], \n
              \t\t\t\t\t"\<  dt=\>", \ dt, \ "\<   dx=  \>", dx], \n\t\t\t\t\ 
            \n\t\ \ \ \ \ k = 0, 
            \ \  (*\ counter\ for\ Tcurrent\  = k\ dt*) \n\t\t\ \ \ \ \ \ \ 
            For[j = 0, \ j < n, \(j++\), u[j] = g[j*dx]\ ], v[0] = 0.0, \ 
            s[0] = 0.0, \n\t\t\ \ \ 
            While[\((k = k + 1)\) < n - 4, \n
              \t\t\t\t\t{\ 
                \[Lambda][k] = 
                  \[Theta] + \ 
                    \((2  \[Theta]\ u[1] + 
                          \((1 - 2  \[Theta])\) \((u[2] - 4  u[1])\) + \n
                          \t\t\t\t\t\t\t\t\t\t\ \ \ \ 
                          3  \[Alpha]*dt*\ Exp[\[Alpha]*k*dt]\ )\)/
                      \((u[3] - 4\ u[2] - u[1])\), \n
                \ \ \ \ \ \ \ \ \ \ \ \ \ \ 
                s[k] = s[k - 1] - \[Lambda][k]*2*dx - \((\[Alpha] - 1)\) dt, 
                \n\t\ \ \ \ \ \ \ \ \ 
                For[j = 1, j < n - k, \(j++\), \n
                  \t\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 
                  v[j] = \((1 - 2  \[Theta])\) u[j] + \ 
                      \((\[Theta] + \[Lambda][k])\) u[j - 1] + \n
                      \t\t\t\t\t\t\t\ \ \ \ \ \ 
                      \((\[Theta] - \[Lambda][k])\) u[j + 1] - 
                      \[Alpha]\ *dt*\ Exp[\[Alpha]*k*dt]\ ], \n
                \ \ \ \ \ \ \ \ \ k = k + 1, \n\t\t\t\t\ \ \ 
                \[Lambda][k] = 
                  \[Theta] + \ 
                    \((2  \[Theta]\ v[1] + 
                          \((1 - 2  \[Theta])\) \((v[2] - 4  v[1])\) + \n
                          \t\t\t\t\t\t\t\t\t\t\ \ 
                          3  \[Alpha]*dt*\ Exp[\[Alpha]*k*dt]\ )\)/
                      \((v[3] - 4\ v[2] - v[1])\), \n\ \ \ \ \ \ \ \ \ \ \ \ 
                s[k] = s[k - 1] - \[Lambda][k]*2*dx - \((\[Alpha] - 1)\) dt, 
                \n\t\ \ \ \ \ \ \ \ \ \ 
                For[j = 1, j < n - k, \(j++\), \n
                  \t\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 
                  u[j] = \((1 - 2  \[Theta])\)\ v[j] + \ 
                      \((\[Theta] + \[Lambda][k])\) v[j - 1] + \n
                      \t\t\t\t\t\t\t\ \ \ \ \ \ \ \ \ \ \ \ 
                      \((\[Theta] - \[Lambda][k])\) v[j + 1] - 
                      \[Alpha]\ *\ dt*\ Exp[\[Alpha]*k*dt]\ ]\n
                \t\t\ \ \ \ \ \ \ \ \ \ \ }], \  (*\ end\ of\ \ k\ loop\ *) \n
            \n\t\t\t\t\ 
            S[mt, mx] = 
              Table[{k*dt*2/\[Sigma]^2, \ Exp[s[k]]\ }, {k, 5 \((n - 4)\)/12, 
                  n - 4, \((n - 4)\)/12}\ ], \n\t\t\t\t\t\ 
            S1[mt, mx] = 
              Table[{k*dt*2/\[Sigma]^2, \ Exp[s[k]]\ }, {k, 4 \((n - 4)\)/12, 
                  n - 4, \((n - 4)\)/12}\ ], \n\t\t\t\t\ 
            ST1[mx] = Join[ST1[mx], S1[mt, mx]], \n\t\t\t\t\ 
            ST[mx] = Join[ST[mx], S[mt, mx]]\n\t\t\n\t\t\t\t\t\ \ }], 
        \ \  (*end\ of\ mt\ Loop\ *) \n
        \t\t\ \ \  (*\ \ \ \ Print[ST1[mx]], \ *) \ \ \ \ \n\t\t\ \ \ \ \ 
        SlogT[mx] = 
          Table[\ {Log[10, \(ST[mx]\)[\([k, 1]\)]], \(ST[mx]\)[\([k, 2]\)]}, {
              k, 1, Length[ST[mx]]}], \n\t\t\ \ \ \ 
        SlogT1[mx] = 
          Table[\ {Log[10, \(ST1[mx]\)[\([k, 1]\)]], 
              \(ST1[mx]\)[\([k, 2]\)]}, {k, 1, Length[ST1[mx]]}], \n\t\t\n
        \t\t\ \ \ \ ListPlot[SlogT1[mx]]\n\t\t\ \ \ \ \ \ \ \ \n\t\t}]\  (*
      end\ of\ mx\ loop*) \n\n\n\t\t\), 
    \(mx = 1; \n
    While[\((mx = mx + 1)\) < mxMax, \n
      \t{SInt[mx] = 
          Table[{\(ST[0]\)[\([k, 1]\)], 
              interpo[\(ST[mx - 2]\)[\([k, 2]\)], \(ST[mx - 1]\)[\([k, 2]\)], 
                \(ST[mx]\)[\([k, 2]\)]]}, {k, 1, Length[ST[0]]}], \n\t
        SIntlogT[mx] = 
          Table[{Log[10, \(ST[0]\)[\([k, 1]\)]], 
              interpo[\(ST[mx - 2]\)[\([k, 2]\)], \(ST[mx - 1]\)[\([k, 2]\)], 
                \(ST[mx]\)[\([k, 2]\)]]}, {k, 1, Length[ST[0]]}], \n\t
        SInt1[mx] = 
          Table[{\(ST1[0]\)[\([k, 1]\)], 
              interpo[\(ST1[mx - 2]\)[\([k, 2]\)], 
                \(ST1[mx - 1]\)[\([k, 2]\)], \(ST1[mx]\)[\([k, 2]\)]]}, {k, 
              1, Length[ST1[0]]}], \n\t
        SIntlogT1[mx] = 
          Table[{Log[10, \(ST1[0]\)[\([k, 1]\)]], 
              interpo[\(ST1[mx - 2]\)[\([k, 2]\)], 
                \(ST1[mx - 1]\)[\([k, 2]\)], \(ST1[mx]\)[\([k, 2]\)]]}, {k, 
              1, Length[ST1[0]]}]}]; \n
    ListPlot[SInt1[mxMax - 1], \ PlotRange -> All]\), 
    \(ListPlot[SIntlogT1[mxMax - 1], PlotRange -> All]\n\t\), 
    \(mx = \(-1\); \n\t\t
    While[\((mx = mx + 1)\) < mxMax, \n
      \t{Er[mx] = 
          Table[{Log[10, \(ST1[0]\)[\([k, 1]\)]], \ 
              \(ST1[mx]\)[\([k, 2]\)] - \(SInt1[mxMax - 1]\)[\([k, 2]\)]}, {
              k, 1, Length[ST1[0]]}], \n
        logEr[mx] = 
          Table[{Log[10, \(ST1[0]\)[\([k, 1]\)]], 
              Log[10, Abs[\ 
                  \(ST1[mx]\)[\([k, 2]\)] - 
                    \(SInt1[mxMax - 1]\)[\([k, 2]\)]]]}, {k, 1, 
              Length[ST1[0]]}], \n\t\tListPlot[Er[mx], PlotRange -> All], \n
        \t\tListPlot[logEr[mx], PlotRange -> All]}]; \nmx = 1; \n\t\t
    While[\((mx = mx + 1)\) < mxMax - 1, \n
      \t{ErInt[mx] = 
          Table[{Log[10, \(ST1[0]\)[\([k, 1]\)]], \ 
              \(SInt1[mx]\)[\([k, 2]\)] - \(SInt1[mxMax - 1]\)[\([k, 2]\)]}, {
              k, 1, Length[ST1[0]]}], \n
        logErInt[mx] = 
          Table[{Log[10, \(ST1[0]\)[\([k, 1]\)]], 
              Log[10, Abs[\ 
                  \(SInt1[mx]\)[\([k, 2]\)] - 
                    \(SInt1[mxMax - 1]\)[\([k, 2]\)]]]}, {k, 1, 
              Length[ST1[0]]}], ListPlot[ErInt[mx], PlotRange -> All], 
        ListPlot[logErInt[mx], PlotRange -> All]}]; \nSInt[mxMax - 1]\), 
    \(SInt1[mxMax - 1]\), 
    \(Table[
      \ {\(logErInt[mxMax - 2]\)[\([k*9]\)], 
        \(logErInt[mxMax - 2]\)[\([k*9 + 1]\)], 
        \(logErInt[mxMax - 2]\)[\([k*9, 2]\)] - 
          \(logErInt[mxMax - 2]\)[\([k*9 + 1, 2]\)]}, \n\t\t\t{k, 1, 16}]\n\n
    \)}], "Input"],

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