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- #1

$\begin{aligned} & {{u}_{tt}}={{u}_{xx}},\text{ }x\in [0,1],\text{ }t>0, \\

& u(x,0)=f(x), \\

& {{u}_{t}}(x,0)=0,\text{ }u(0,t)=u(1,t)=0 \\

\end{aligned}

$

where $f(x)$ is defined by $f(x)=x$ if $0\le x\le \dfrac12$ and $f(x)=1-x$ if $\dfrac12\le x\le1.$

I'm not sure how to proceed here, what's the standard way?