Strang splitting schemes forN-level Bloch models

Abstract

In this paper, we define a splitting scheme for the N-level Bloch model which makes use of exact numerical solutions of sub-equations. These exact solutions involve matrix exponentials which we want to avoid to calculate at each time-step. The resulting scheme is nonstandard and preserves qualitative properties of the Bloch equations. We explore and compare numerically multiple ways to implement it and in particular take into account the specific structure of the Bloch equations.