\newcommand{\lhsI}{
&\displaystyle -{{2\,w_{i+{{1}\over{2}},j}\,N_{i+{{1}\over{2}},j}\,
 \left({{\Delta_y\left(v_{i+1,j}\right)+\Delta_y\left(v_{i,j}\right)
 }\over{4\,\Delta y}}+{{2\,\delta_{+x}\left(u_{i,j}\right)}\over{
 \Delta x}}\right)}\over{\Delta x}} & \\
&\displaystyle -{{w_{i,j+{{1}\over{2}}}\,N_{i,j+{{1}\over{2}}}\,
 \left({{\Delta_x\left(v_{i,j+1}\right)+\Delta_x\left(v_{i,j}\right)
 }\over{4\,\Delta x}}+{{\delta_{+y}\left(u_{i,j}\right)}\over{
 \Delta y}}\right)}\over{\Delta y}} & \\
&\displaystyle {{2\,w_{i-{{1}\over{2}},j}\,N_{i-{{1}\over{2}},j}\,
 \left({{\Delta_y\left(v_{i,j}\right)+\Delta_y\left(v_{i-1,j}\right)
 }\over{4\,\Delta y}}+{{2\,\delta_{-x}\left(u_{i,j}\right)}\over{
 \Delta x}}\right)}\over{\Delta x}} & \\
&\displaystyle {{w_{i,j-{{1}\over{2}}}\,N_{i,j-{{1}\over{2}}}\,\left(
 {{\Delta_x\left(v_{i,j}\right)+\Delta_x\left(v_{i,j-1}\right)}\over{
 4\,\Delta x}}+{{\delta_{-y}\left(u_{i,j}\right)}\over{\Delta y}}
 \right)}\over{\Delta y}} & \\
}
\newcommand{\lhsII}{
&\displaystyle -{{w_{i+{{1}\over{2}},j}\,N_{i+{{1}\over{2}},j}\,
 \left({{\Delta_y\left(u_{i+1,j}\right)+\Delta_y\left(u_{i,j}\right)
 }\over{4\,\Delta y}}+{{\delta_{+x}\left(v_{i,j}\right)}\over{
 \Delta x}}\right)}\over{\Delta x}} & \\
&\displaystyle -{{2\,w_{i,j+{{1}\over{2}}}\,N_{i,j+{{1}\over{2}}}\,
 \left({{\Delta_x\left(u_{i,j+1}\right)+\Delta_x\left(u_{i,j}\right)
 }\over{4\,\Delta x}}+{{2\,\delta_{+y}\left(v_{i,j}\right)}\over{
 \Delta y}}\right)}\over{\Delta y}} & \\
&\displaystyle {{2\,w_{i,j-{{1}\over{2}}}\,N_{i,j-{{1}\over{2}}}\,
 \left({{2\,\delta_{-y}\left(v_{i,j}\right)}\over{\Delta y}}+{{
 \Delta_x\left(u_{i,j}\right)+\Delta_x\left(u_{i,j-1}\right)}\over{4
 \,\Delta x}}\right)}\over{\Delta y}} & \\
&\displaystyle {{w_{i-{{1}\over{2}},j}\,N_{i-{{1}\over{2}},j}\,\left(
 {{\delta_{-x}\left(v_{i,j}\right)}\over{\Delta x}}+{{\Delta_y\left(u
 _{i,j}\right)+\Delta_y\left(u_{i-1,j}\right)}\over{4\,\Delta y}}
 \right)}\over{\Delta x}} & \\
}
\newcommand{\lhsIII}{
&\displaystyle -{{2\,w_{i+{{1}\over{2}},j}\,N_{i+{{1}\over{2}},j}\,
 \left({{w_{i+1,j-{{1}\over{2}}}\,\delta_{{\it -y}}(v_{i+1,j})+w_{i+1
 ,j+{{1}\over{2}}}\,\delta_{{\it +y}}(v_{i+1,j})+w_{i,j-{{1}\over{2}}
 }\,\delta_{{\it -y}}(v_{i,j})+w_{i,j+{{1}\over{2}}}\,\delta_{
 {\it +y}}(v_{i,j})}\over{4\,\Delta y}}+{{2\,w_{i+{{1}\over{2}},j}\,
 \delta_{{\it +x}}(u_{i,j})}\over{\Delta x}}\right)}\over{\Delta x}} & \\
&\displaystyle -{{w_{i,j+{{1}\over{2}}}\,N_{i,j+{{1}\over{2}}}\,
 \left({{w_{i-{{1}\over{2}},j+1}\,\delta_{{\it -x}}(v_{i,j+1})+w_{i+
 {{1}\over{2}},j+1}\,\delta_{{\it +x}}(v_{i,j+1})+w_{i-{{1}\over{2}},
 j}\,\delta_{{\it -x}}(v_{i,j})+w_{i+{{1}\over{2}},j}\,\delta_{
 {\it +x}}(v_{i,j})}\over{4\,\Delta x}}+{{w_{i,j+{{1}\over{2}}}\,
 \delta_{{\it +y}}(u_{i,j})}\over{\Delta y}}\right)}\over{\Delta y}} & \\
&\displaystyle {{2\,w_{i-{{1}\over{2}},j}\,N_{i-{{1}\over{2}},j}\,
 \left({{w_{i,j-{{1}\over{2}}}\,\delta_{{\it -y}}(v_{i,j})+w_{i,j+{{1
 }\over{2}}}\,\delta_{{\it +y}}(v_{i,j})+w_{i-1,j-{{1}\over{2}}}\,
 \delta_{{\it -y}}(v_{i-1,j})+w_{i-1,j+{{1}\over{2}}}\,\delta_{
 {\it +y}}(v_{i-1,j})}\over{4\,\Delta y}}+{{2\,w_{i-{{1}\over{2}},j}
 \,\delta_{{\it -x}}(u_{i,j})}\over{\Delta x}}\right)}\over{\Delta x
 }} & \\
&\displaystyle {{w_{i,j-{{1}\over{2}}}\,N_{i,j-{{1}\over{2}}}\,\left(
 {{w_{i-{{1}\over{2}},j}\,\delta_{{\it -x}}(v_{i,j})+w_{i+{{1}\over{2
 }},j}\,\delta_{{\it +x}}(v_{i,j})+w_{i-{{1}\over{2}},j-1}\,\delta_{
 {\it -x}}(v_{i,j-1})+w_{i+{{1}\over{2}},j-1}\,\delta_{{\it +x}}(v_{i
 ,j-1})}\over{4\,\Delta x}}+{{w_{i,j-{{1}\over{2}}}\,\delta_{{\it -y}
 }(u_{i,j})}\over{\Delta y}}\right)}\over{\Delta y}} & \\
}
\newcommand{\CUfirstInterior}{
&-1 & 0 & 1 \\\hline
\hline
$1$
&$\displaystyle 0$
&$\displaystyle -{{c_{n}}\over{\Delta y^2}}$
&$\displaystyle 0$
\\
\hline
$0$
&$\displaystyle -{{4\,c_{w}}\over{\Delta x^2}}$
&$\displaystyle {{c_{s}+c_{n}}\over{\Delta y^2}}+{{4\,\left(c_{w}+
 c_{e}\right)}\over{\Delta x^2}}$
&$\displaystyle -{{4\,c_{e}}\over{\Delta x^2}}$
\\
\hline
$-1$
&$\displaystyle 0$
&$\displaystyle -{{c_{s}}\over{\Delta y^2}}$
&$\displaystyle 0$
\\
}
\newcommand{\CUsecondInterior}{
&-1 & 0 & 1 \\\hline
\hline
$1$
&$\displaystyle {{c_{w}+2\,c_{n}}\over{4\,\Delta x\,\Delta y}}$
&$\displaystyle {{c_{w}-c_{e}}\over{4\,\Delta x\,\Delta y}}$
&$\displaystyle -{{2\,c_{n}+c_{e}}\over{4\,\Delta x\,\Delta y}}$
\\
\hline
$0$
&$\displaystyle -{{c_{s}-c_{n}}\over{2\,\Delta x\,\Delta y}}$
&$\displaystyle 0$
&$\displaystyle {{c_{s}-c_{n}}\over{2\,\Delta x\,\Delta y}}$
\\
\hline
$-1$
&$\displaystyle -{{c_{w}+2\,c_{s}}\over{4\,\Delta x\,\Delta y}}$
&$\displaystyle -{{c_{w}-c_{e}}\over{4\,\Delta x\,\Delta y}}$
&$\displaystyle {{2\,c_{s}+c_{e}}\over{4\,\Delta x\,\Delta y}}$
\\
}
\newcommand{\CVfirstInterior}{
&-1 & 0 & 1 \\\hline
\hline
$1$
&$\displaystyle {{2\,c_{w}+c_{n}}\over{4\,\Delta x\,\Delta y}}$
&$\displaystyle {{c_{w}-c_{e}}\over{2\,\Delta x\,\Delta y}}$
&$\displaystyle -{{c_{n}+2\,c_{e}}\over{4\,\Delta x\,\Delta y}}$
\\
\hline
$0$
&$\displaystyle -{{c_{s}-c_{n}}\over{4\,\Delta x\,\Delta y}}$
&$\displaystyle 0$
&$\displaystyle {{c_{s}-c_{n}}\over{4\,\Delta x\,\Delta y}}$
\\
\hline
$-1$
&$\displaystyle -{{2\,c_{w}+c_{s}}\over{4\,\Delta x\,\Delta y}}$
&$\displaystyle -{{c_{w}-c_{e}}\over{2\,\Delta x\,\Delta y}}$
&$\displaystyle {{c_{s}+2\,c_{e}}\over{4\,\Delta x\,\Delta y}}$
\\
}
\newcommand{\CVsecondInterior}{
&-1 & 0 & 1 \\\hline
\hline
$1$
&$\displaystyle 0$
&$\displaystyle -{{4\,c_{n}}\over{\Delta y^2}}$
&$\displaystyle 0$
\\
\hline
$0$
&$\displaystyle -{{c_{w}}\over{\Delta x^2}}$
&$\displaystyle {{4\,\left(c_{s}+c_{n}\right)}\over{\Delta y^2}}+{{
 c_{w}+c_{e}}\over{\Delta x^2}}$
&$\displaystyle -{{c_{e}}\over{\Delta x^2}}$
\\
\hline
$-1$
&$\displaystyle 0$
&$\displaystyle -{{4\,c_{s}}\over{\Delta y^2}}$
&$\displaystyle 0$
\\
}
\newcommand{\CUfirstMargin}{
&-1 & 0 & 1 \\\hline
\hline
$1$
&$\displaystyle 0$
&$\displaystyle -{{c_{n}\,{\it bPP}^2}\over{\Delta y^2}}$
&$\displaystyle 0$
\\
\hline
$0$
&$\displaystyle -{{4\,c_{w}\,{\it aMM}^2}\over{\Delta x^2}}$
&$\displaystyle {{c_{n}\,{\it bPP}^2+c_{s}\,{\it bMM}^2}\over{
 \Delta y^2}}+{{4\,\left(c_{e}\,{\it aPP}^2+c_{w}\,{\it aMM}^2\right)
 }\over{\Delta x^2}}$
&$\displaystyle -{{4\,c_{e}\,{\it aPP}^2}\over{\Delta x^2}}$
\\
\hline
$-1$
&$\displaystyle 0$
&$\displaystyle -{{c_{s}\,{\it bMM}^2}\over{\Delta y^2}}$
&$\displaystyle 0$
\\
}
\newcommand{\CUsecondMargin}{
C^{u,2}_{-1,-1} &=& \displaystyle -{{c_{w}\,{\it aMM}\,{\it bMw}}\over{4\,\Delta x\,\Delta y}} \\
&+& \displaystyle -{{c_{s}\,{\it aMs}\,{\it bMM}}\over{2\,\Delta x\,\Delta y}} \\
C^{u,2}_{-1,0} &=& \displaystyle {{c_{w}\,{\it aMM}\,\left({\it bMw}-{\it bPw}\right)}\over{4\,\Delta x\,\Delta y}} \\
&+& \displaystyle {{{\it aMM}\,\left(c_{n}\,{\it bPP}-c_{s}\,{\it bMM}\right)}\over{2\,\Delta x\,\Delta y}} \\
C^{u,2}_{-1,1} &=& \displaystyle {{c_{w}\,{\it aMM}\,{\it bPw}}\over{4\,\Delta x\,\Delta y}} \\
&+& \displaystyle {{c_{n}\,{\it aMn}\,{\it bPP}}\over{2\,\Delta x\,\Delta y}} \\
C^{u,2}_{0,-1} &=& \displaystyle {{c_{s}\,\left({\it aMs}-{\it aPs}\right)\,{\it bMM}}\over{2\,\Delta x\,\Delta y}} \\
&+& \displaystyle {{\left(c_{e}\,{\it aPP}-c_{w}\,{\it aMM}\right)\,{\it bMM}}\over{4\,\Delta x\,\Delta y}} \\
C^{u,2}_{0,0} &=& \displaystyle {{c_{n}\,\left({\it aPP}-{\it aMM}\right)\,{\it bPP}+c_{s}\,\left({\it aMM}-{\it aPP}\right)\,{\it bMM}}\over{2\,\Delta x\,\Delta y}} \\
&+& \displaystyle {{\left(c_{e}\,{\it aPP}-c_{w}\,{\it aMM}\right)\,{\it bPP}+\left(c_{w}\,{\it aMM}-c_{e}\,{\it aPP}\right)\,{\it bMM}}\over{4\,\Delta x\,\Delta y}} \\
C^{u,2}_{0,1} &=& \displaystyle {{c_{n}\,\left({\it aPn}-{\it aMn}\right)\,{\it bPP}}\over{2\,\Delta x\,\Delta y}} \\
&+& \displaystyle {{\left(c_{w}\,{\it aMM}-c_{e}\,{\it aPP}\right)\,{\it bPP}}\over{4\,\Delta x\,\Delta y}} \\
C^{u,2}_{1,-1} &=& \displaystyle {{c_{e}\,{\it aPP}\,{\it bMe}}\over{4\,\Delta x\,\Delta y}} \\
&+& \displaystyle {{c_{s}\,{\it aPs}\,{\it bMM}}\over{2\,\Delta x\,\Delta y}} \\
C^{u,2}_{1,0} &=& \displaystyle {{c_{e}\,{\it aPP}\,\left({\it bPe}-{\it bMe}\right)}\over{4\,\Delta x\,\Delta y}} \\
&+& \displaystyle {{{\it aPP}\,\left(c_{s}\,{\it bMM}-c_{n}\,{\it bPP}\right)}\over{2\,\Delta x\,\Delta y}} \\
C^{u,2}_{1,1} &=& \displaystyle -{{c_{e}\,{\it aPP}\,{\it bPe}}\over{4\,\Delta x\,\Delta y}} \\
&+& \displaystyle -{{c_{n}\,{\it aPn}\,{\it bPP}}\over{2\,\Delta x\,\Delta y}} \\
}
\newcommand{\CVfirstMargin}{
C^{v,1}_{-1,-1} &=& \displaystyle -{{c_{w}\,{\it aMM}\,{\it bMw}}\over{2\,\Delta x\,\Delta y}} \\
&+& \displaystyle -{{c_{s}\,{\it aMs}\,{\it bMM}}\over{4\,\Delta x\,\Delta y}} \\
C^{v,1}_{-1,0} &=& \displaystyle {{c_{w}\,{\it aMM}\,\left({\it bMw}-{\it bPw}\right)}\over{2\,\Delta x\,\Delta y}} \\
&+& \displaystyle {{{\it aMM}\,\left(c_{n}\,{\it bPP}-c_{s}\,{\it bMM}\right)}\over{4\,\Delta x\,\Delta y}} \\
C^{v,1}_{-1,1} &=& \displaystyle {{c_{w}\,{\it aMM}\,{\it bPw}}\over{2\,\Delta x\,\Delta y}} \\
&+& \displaystyle {{c_{n}\,{\it aMn}\,{\it bPP}}\over{4\,\Delta x\,\Delta y}} \\
C^{v,1}_{0,-1} &=& \displaystyle {{c_{s}\,\left({\it aMs}-{\it aPs}\right)\,{\it bMM}}\over{4\,\Delta x\,\Delta y}} \\
&+& \displaystyle {{\left(c_{e}\,{\it aPP}-c_{w}\,{\it aMM}\right)\,{\it bMM}}\over{2\,\Delta x\,\Delta y}} \\
C^{v,1}_{0,0} &=& \displaystyle {{c_{n}\,\left({\it aPP}-{\it aMM}\right)\,{\it bPP}+c_{s}\,\left({\it aMM}-{\it aPP}\right)\,{\it bMM}}\over{4\,\Delta x\,\Delta y}} \\
&+& \displaystyle {{\left(c_{e}\,{\it aPP}-c_{w}\,{\it aMM}\right)\,{\it bPP}+\left(c_{w}\,{\it aMM}-c_{e}\,{\it aPP}\right)\,{\it bMM}}\over{2\,\Delta x\,\Delta y}} \\
C^{v,1}_{0,1} &=& \displaystyle {{c_{n}\,\left({\it aPn}-{\it aMn}\right)\,{\it bPP}}\over{4\,\Delta x\,\Delta y}} \\
&+& \displaystyle {{\left(c_{w}\,{\it aMM}-c_{e}\,{\it aPP}\right)\,{\it bPP}}\over{2\,\Delta x\,\Delta y}} \\
C^{v,1}_{1,-1} &=& \displaystyle {{c_{e}\,{\it aPP}\,{\it bMe}}\over{2\,\Delta x\,\Delta y}} \\
&+& \displaystyle {{c_{s}\,{\it aPs}\,{\it bMM}}\over{4\,\Delta x\,\Delta y}} \\
C^{v,1}_{1,0} &=& \displaystyle {{c_{e}\,{\it aPP}\,\left({\it bPe}-{\it bMe}\right)}\over{2\,\Delta x\,\Delta y}} \\
&+& \displaystyle {{{\it aPP}\,\left(c_{s}\,{\it bMM}-c_{n}\,{\it bPP}\right)}\over{4\,\Delta x\,\Delta y}} \\
C^{v,1}_{1,1} &=& \displaystyle -{{c_{e}\,{\it aPP}\,{\it bPe}}\over{2\,\Delta x\,\Delta y}} \\
&+& \displaystyle -{{c_{n}\,{\it aPn}\,{\it bPP}}\over{4\,\Delta x\,\Delta y}} \\
}
\newcommand{\CVsecondMargin}{
&-1 & 0 & 1 \\\hline
\hline
$1$
&$\displaystyle 0$
&$\displaystyle -{{4\,c_{n}\,{\it bPP}^2}\over{\Delta y^2}}$
&$\displaystyle 0$
\\
\hline
$0$
&$\displaystyle -{{c_{w}\,{\it aMM}^2}\over{\Delta x^2}}$
&$\displaystyle {{4\,\left(c_{n}\,{\it bPP}^2+c_{s}\,{\it bMM}^2
 \right)}\over{\Delta y^2}}+{{c_{e}\,{\it aPP}^2+c_{w}\,{\it aMM}^2
 }\over{\Delta x^2}}$
&$\displaystyle -{{c_{e}\,{\it aPP}^2}\over{\Delta x^2}}$
\\
\hline
$-1$
&$\displaystyle 0$
&$\displaystyle -{{4\,c_{s}\,{\it bMM}^2}\over{\Delta y^2}}$
&$\displaystyle 0$
\\
}
