 Solution

A numerical evolution has numerical stability if small perturbations in initial data, forcing or arithmetic are not amplified without control over the time interval of interest. For this constant-coefficient decaying linear system, an absolute-stability test requires the homogeneous numerical amplification factors to have magnitude at most one, with no growing Jordan-block contribution on the unit circle. Stability is distinct from accuracy: a strongly overdamped numerical solution can be stable while representing the physical oscillation poorly.