Apply the numerical method to the test equation $y'=\lambda y$ and put $z=h\lambda$. Its <linear stability domain> is the set of $z$ for which the computed amplification is stable, for a one-step method $|R(z)|\le1$ with all stage solves well-defined. The method is <A-stable> if this includes the whole closed left half-plane (or its interior with boundary limits).

Solution

Past exam of the mathematics course of the University of Cambridge / 2007 / ii / Paper 1 / 38C / a / Solution

 Solution (source code)