# Unconditionally convergent scheme for $u_t = \Delta u - u$ under certain condition

I am looking for an unconditionally stable, convergent finite difference scheme for $$u_t = \Delta u - u$$ on the cube $0 \leq x,y,z \leq 1$ with $t > 0$ and a zero boundary condition on the boundary, smooth initial data. However, the kicker is that the scheme should only involve inverting $n \times n$ matrices where $n$ is the number of grid points per direction. Meaning in the x direction, there are the grid points $x_1, x_2, \dots, x_n.$

The first thought that comes to head immediately after seeing the equation is using forward in time, and centered in space for the second derivatives, such as $$u_{xx} \approx \frac{u(x-h) - 2u(x) + u(x+h)}{h^2}.$$ Once discretized, one sees that one needs data from the $x_0$ and $x_{n+1}$ grid points. Perhaps there is a way to treat the boundary condition so that this isn't the case? Any suggestions on this thought? Any help at all is appreciated! Thanks.