More precisely, Pasch [118Jump To The Next Citation Point] found that that an exponential integrator worked well when the flow’s Jacobian matrix was computed exactly (using the symbolic-differentiation technique described in Section 8.5.4). However, when the Jacobian matrix was approximated using the numerical-perturbation technique described in Section 8.5.4, Pasch found that the pseudo-time integration became unstable at high numerical resolutions. Pasch [118Jump To The Next Citation Point] also notes that the exponential integrator uses a very large amount of memory.