Consider the partial differential equation

$\frac{\text{d}\text{e}\text{l}\text{u}}{\text{d}\text{e}\text{l}\text{t}}+c\frac{\text{d}\text{e}\text{l}\text{u}}{\text{d}\text{e}\text{l}\text{x}}=0$

An explicit finite difference representation of this equation can be written as

$u_{i,n+1}=u_{i,n}-\frac{}{2}[u_{i+1,n}-u_{i-1,n}]$

where $=\frac{ct}{x},$ Perform a Von Neumann stability analysis to show that this finite difference equation is unconditionally unstable.