I'm trying to find the asymptotic behavior of the follow system of 100 differential equation:
$x'_i=x_{i-1}+x_{i+1}-2x_i, 1\leq i \leq 100\\ x_0 = x_{101}=0$
I'm trying to find the asymptotic behavior of this and am not sure of where to even begin. I believe I need to find the growth and decay rates of the equations.