Past exam of the short options paper shared by Parts A and B of the physics course of the University of Oxford / 2019 / S31 / 3 / d

Backward Euler method has update ${\mathbf{y}}^{n+1}=(I-hM{)}^{-1}{\mathbf{y}}^n$ and amplification eigenvalues $g_{\pm }=(1-h{\lambda }_{\pm }{)}^{-1}$. Hencefor every $h\ge 0$. It is therefore unconditionally stable for this linear system. Even with $\gamma =0$, it damps every nonzero numerical mode: stability is obtained at the cost of artificial damping and phase error. Large $h$ does not accurately resolve the oscillation period.