Loading [MathJax]/extensions/TeX/boldsymbol.js
\newcommand{\uex}{{u_{\small\mbox{e}}}}
\newcommand{\half}{\frac{1}{2}}
\newcommand{\halfi}{{1/2}}
\newcommand{\xpoint}{\boldsymbol{x}}
\newcommand{\normalvec}{\boldsymbol{n}}
\newcommand{\Oof}[1]{\mathcal{O}(#1)}
\newcommand{\Ix}{\mathcal{I}_x}
\newcommand{\Iy}{\mathcal{I}_y}
\newcommand{\It}{\mathcal{I}_t}
\newcommand{\setb}[1]{#1^0} % set begin
\newcommand{\sete}[1]{#1^{-1}} % set end
\newcommand{\setl}[1]{#1^-}
\newcommand{\setr}[1]{#1^+}
\newcommand{\seti}[1]{#1^i}
\newcommand{\Real}{\mathbb{R}}
Index set notation
- Tedious to write index sets like i=0,\ldots,N_x and
n=0,\ldots,N_t
- Notation not valid if i or n starts at 1 instead...
- Both in math and code it is advantageous to use index sets
- i\in\Ix instead of i=0,\ldots,N_x
- Definition: \Ix =\{0,\ldots,N_x\}
- The first index: i=\setb{\Ix}
- The last index: i=\sete{\Ix}
- All interior points: i\in\seti{\Ix} , \seti{\Ix}=\{1,\ldots,N_x-1\}
- \setl{\Ix} means \{0,\ldots,N_x-1\}
- \setr{\Ix} means \{1,\ldots,N_x\}
