In this paper, differential conductivity and reluctivity matrices are constructed for formulations discretised by the finite integration technique and linearised by the Newton method. It turns out that these matrices are nondiagonal and unsymmetric, even in the case that orthogonal grids are used. A diagonal approximation of the differential matrices leads to an approximate Newton method where cross-magnetisation effects are no longer considered, except in the update between the successive nonlinear iteration steps. The approximate method does not guarantee second order convergence but outperforms the true Newton method when only a moderate accuracy is required.