Implicit ODE solvers are not universally more robust than explicit ODE solvers
A very common adage in ODE solvers is that if you run into trouble with an explicit method, usually some explicit Runge-Kutta method like RK4, then you should try an implicit method. Implicit methods, because they are doing more work, solving an implicit system via a Newton method having “better” stability, should be the thing you go to on the “hard” problems. This is at least what I heard at first, and then I learned about edge cases. Specifically, you hear people say “but for hyperbolic PDEs