Before revision:  The complex-step approximation of the Jacobian is applied to the Krylov-based KIOPS (Krylov with incomplete orthogonalization procedure solver) algorithm for computing matrix-vector products with \varphi -functions.
After revision:  The complex-step approximation of the Jacobian in the Krylov-based KIOPS (Krylov with incomplete orthogonalization procedure solver) algorithm for computing matrix-vector products with \varphi -functions.