Set up the comparable problem using the first central difference approximation for $\frac{f^{2}u}{f{x}^2},$ i$.$e$.$ derive arrays $M$ and $K$ in the system of equations represented by

$M\frac{dx}{dt}+Kx=f(t),=>x^{j+1}=x^j-M^{-1}[Kx+f(t^j)]t$

This is the implicit Euler algorithm