Adjusting the Boundary Condition Locations for the 1D Wave Equation I'm trying to solve the non-dimensional 1D wave equation:
$\frac{\partial^2 u}{\partial x^2}=\frac{\partial^2 u}{\partial t^2}$
subject to the homogenous Dirichlet boundary conditions. However the interval for the problem is not the usual $0\leq x \leq L$, but rather $-4 \leq x \leq 5$. 
Can I adjust this range by shifting it +4 so that it goes from $0\leq x \leq 9$ and use that as the location of the boundaries? Using the original BCs seems to lead to a more tedious and involved solution. 
Boundary Conditions:
$u(-4,t)=u(5,t)=0$
Initial Conditions:
$u(x,0)=sin(\pi x) $ for $ 0 \leq x \leq 1$ and $0$ everywhere else.
$\frac{\partial u(x,0)}{\partial t} = 0$

Yes, since your equation does not depend on $x$.
You have to shift the initial condition, though, since it depends on $x$. Use $$u(x,0)=\sin(\pi(x+4))$$ on $4\leq x \leq 5$ and $0$ everywhere else. Of course, if you shift the equation, you have to shift the initial condition as well. The solution will also be shifted into the new domain, obviously.
I hope I got your question right now. 
