stiff equation
An ODE where an EXPLICIT method's stability (not its accuracy) is what actually forces the step size to be tiny.
An initial-value problem is stiff when its stability requirement -- h\lambda staying inside the method's own region of absolute stability, for the fastest-decaying component of the solution -- forces a far smaller h than accuracy alone would ever demand. A stiff equation is perfectly well-posed and its true solution may be smooth and slowly varying; the difficulty is entirely in what an EXPLICIT method's own limited stability region requires, not in the mathematics of the problem itself. Implicit methods, with far larger (sometimes unconditionally stable) regions, are the standard remedy.
Examples
A chemical-kinetics system with one very fast reaction and one very slow one is a classic stiff equation: the fast reaction forces a tiny h on an explicit method even after it has long since died out.
See also