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The partial differential equation for the vector-potential of heteropolar machines is established taking into account the non-linearities of the materials and the current distributions. The non-linear equation, similar to Poisson's equation, is transformed into a partial difference equation. The magnetic induction is found at discrete points in the cross section of the machine. A new relaxation procedure, accelerated greatly by the use of a new physical method of adjusting the vector potential between two successive iterations, is used. The method is shown for an aerospace synchronous generator. Calculated and test results of the no-load characteristic agree quite well. Pole tip saturation is fully considered.