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[en] A method for approximately solving magnetic differential equations is described. The approach is to include a small diffusion term to the equation, which regularizes the linear operator to be inverted. The extra term allows a 'source-correction' term to be defined, which is generally required in order to satisfy the solvability conditions. The approach is described in the context of computing the pressure and parallel currents in the iterative approach for computing magnetohydrodynamic equilibria.