$(25$pts$.)$ Solve the wave equation $u_{tt}=u_x(x,t),$ for $0x1$ and $0t1$ with the boundary

conditions

$u(0,t)=0=u(1,t),0t1$

$u(x,0)=sin(x),0x1$

$u_t(x,0)=0,0x1,$

Choose $h=0\mathrm{.}1$ and $k=0\mathrm{.}1.$

note:Do not solve the

question by hand, write a

Matlab code implementation

to solve the question