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The engineering design of eddy current actuated systems is expensive because of the rapid changes in field quantities and the resulting need to model very accurately. Many suggestions have been made to avoid computations in eddy current regions. The best known of these is the impedance boundary condition at steel interfaces. However, the impedance boundary condition does not work for nonlinear steel because the phasor analysis on which the impedance boundary condition is based is not applicable. MacLean's model is best suited for analyzing in the nonlinear region. Reported problems with time stepping are overcome by studying various time-stepping methods and identifying a suitable numerical scheme. The identified method is shown to be convergent by using the von Neumann stability test.