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The paper presents a formulation for two-dimensional anisotropic eddy current problems developed both in the time and the frequency domains. It is based on the cell method, that makes use of integral electromagnetic quantities related to each other through algebraic constitutive and structure equations. This formulation directly assembles both the so-called stiffness and mass matrices by means of an inspection approach with no need to use topological incidence matrices, thus providing an agile construction of the fundamental system and requiring to compute only the primal cell complex, not the dual one. The formulation is compared with an equivalent finite element method method based on the Galerkin and Crank-Nicolson schemes, both being used for simulating an experimental induction-heating apparatus.