Efficient discretization scheme for semi-analytical solutions of the Bloch-Torrey equation

•Spatial discretization of the Bloch-Torrey equation allows calculation of a Heisenberg-style matrix Hamiltonian which leads to the correct solution over the whole diffusion domain.•Numerical calculation can be easily implemented using this matrix formalism without relying on special functions.•Free induction decay and inhomogeneous relaxation rates obtained using this method agree with known approximations for weak and strong diffusion.