$$
\newcommand{\uex}{{u_{\small\mbox{e}}}}
\newcommand{\half}{\frac{1}{2}}
\newcommand{\halfi}{{1/2}}
\newcommand{\xpoint}{\boldsymbol{x}}
\newcommand{\normalvec}{\boldsymbol{n}}
\newcommand{\Oof}[1]{\mathcal{O}(#1)}
\newcommand{\Ix}{\mathcal{I}_x}
\newcommand{\Iy}{\mathcal{I}_y}
\newcommand{\It}{\mathcal{I}_t}
\newcommand{\setb}[1]{#1^0} % set begin
\newcommand{\sete}[1]{#1^{-1}} % set end
\newcommand{\setl}[1]{#1^-}
\newcommand{\setr}[1]{#1^+}
\newcommand{\seti}[1]{#1^i}
\newcommand{\Real}{\mathbb{R}}
$$
Computing the error in wave velocity
- Introduce \( p=k\Delta x/2 \)
(the important dimensionless spatial discretization parameter)
- \( p \) measures no of mesh points in space
per wave length in space
- Study error in wave velocity through \( \tilde c/c \) as function of \( p \)
$$
r(C, p) = \frac{\tilde c}{c} = \frac{1}{Cp}{\sin}^{-1}\left(C\sin p\right),
\quad C\in (0,1],\ p\in (0,\pi/2]
$$
