- #1
Markov2
- 149
- 0
Solve
$\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?
$\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?