I have the ODE below$$\frac{d}{dt}\pmatrix{x\\ y} = \pmatrix{0 &1\\-a &0}\pmatrix{x\\ y} \enspace .$$The $m=1$ leapfrog method is defined as:$$y_{n+1} = y_{n-1} + 2f_nh \enspace .$$For the $a<0$ state, how do I simply find the condition the solution must satisfy for the method to be successful? Further, how do I enforce this in practice?
The condition for stability using the leapfrog method
computational physics;stability;explicit methods