  There are various situations where the classical Fourier's law for heat
conduction is not applicable, such as heat conduction in heterogeneous
materials or for modeling low-temperature phenomena. 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.
