In this paper, differential conductivity and reluctivity matricesare constructed for formulations discretised by the finiteintegration technique and linearised by the Newton method. It turnsout that these matrices are nondiagonal and unsymmetric, even in thecase that orthogonal grids are used. A diagonal approximation of thedifferential matrices leads to an approximate Newton method wherecross-magnetisation effects are no longer considered, except in theupdate 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.