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Two numerical methods are presented and compared for solution of nonlinear instantaneous electromagnetic diffusion problems. Finite differences are used for discretization of space. The Crank-Nicolson and improved State-Space methods are used for time. A magnetic vector potential (m.v.p.) formulation is used, which is effective in simplifying programming implementation to electrical machinery problems with complex contours. The methods are applied to a practical example of eddy currents, flux penetration and losses, and are found to yield results which are in excellent agreement with experimental test data. The results include a vivid display of the distortive effect of magnetic non-linearity on eddy current and flux density wave forms. The comparative suitability of both methods are evaluated in light of their characteristics and results.