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The time-stepping finite-element method (FEM) has become a powerful tool in solving transient electromagnetic fields. The formulation can include complex issues such as time harmonics and space harmonics, nonlinear magnetic property of iron materials, external circuit, and mechanical motion in the system equations. However, as the derivatives of physical quantities are usually unknown at the initial step of the time-stepping method, erroneous solutions might appear at the beginning of the transient process. To reduce the number of time steps, an adaptive step size algorithm can be used. In this paper, a method to eliminate the nonphysical or nonrealistic solutions at the start of the time-stepping finite-element analysis (FEA), when simulating the transient process of electric devices, is presented. A practical implementation of adaptive time step size algorithm for coupled problems is proposed. A matrix operation method, which can be understood clearly and implemented easily, that deals with matching boundary conditions in the study of mechanical motion, is also described.