Stability of the iterated Crank-Nicholson method in numerical relativity
Saul A. Teukolsky · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · 2000
The iterated Crank-Nicholson method has become a popular algorithm in numerical relativity. We show that one should carry out exactly two iterations and no more. While the limit of an infinite number of iterations is the standard Crank-Nicholson method, it can in fact be worse to do more than two iterations, and it never helps. We explain how this paradoxical result arises.