$$ \newcommand{\uex}{{u_{\small\mbox{e}}}} \newcommand{\half}{\frac{1}{2}} \newcommand{\halfi}{{1/2}} \newcommand{\xpoint}{\boldsymbol{x}} \newcommand{\normalvec}{\boldsymbol{n}} \newcommand{\Oof}[1]{\mathcal{O}(#1)} \newcommand{\Ix}{\mathcal{I}_x} \newcommand{\Iy}{\mathcal{I}_y} \newcommand{\It}{\mathcal{I}_t} \newcommand{\setb}[1]{#1^0} % set begin \newcommand{\sete}[1]{#1^{-1}} % set end \newcommand{\setl}[1]{#1^-} \newcommand{\setr}[1]{#1^+} \newcommand{\seti}[1]{#1^i} \newcommand{\Real}{\mathbb{R}} $$

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Collection of initial conditions

The function pulse in wave1D_dn_vc.py offers four initial conditions:

  1. a rectangular pulse ("plug")

  2. a Gaussian function (gaussian)

  3. a "cosine hat": one period of \( 1 + \cos (\pi x \), \( x\in [-1,1] \)

  4. half a "cosine hat": half a period of \( \cos \pi x \), \( x\in [-{\half},{\half}] \)
Can locate the initial pulse at \( x=0 \) or in the middle 

>>> import wave1D_dn_vc as w
>>> w.pulse(loc='left', pulse_tp='cosinehat', Nx=50, every_frame=10)

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