There are various situations where the classical Fourier's law for heat conduction is not applicable, such as heat conduction in heterogeneous materials (Both et al., 2016; Van et al., 2017) or for modeling low-temperature phenomena (Kovacs and Van, 2015, 2016, 2018). In such cases, heat flux is not directly proportional to temperature gradient, hence, the role - and both the analytical and numerical treatment - of boundary conditions becomes nontrivial. Here, we address this question for finite difference numerics via a shifted field approach. Based on this ground, implicit schemes are presented and compared to each other for the Guyer-Krumhansl generalized heat conduction equation, which successfully describes numerous beyond-Fourier experimental findings. The results are validated by an analytical solution, and are contrasted to finite element method outcomes obtained by COMSOL. (C) 2018 Elsevier Ltd. All rights reserved.