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The electromagnetic inverse source problem (ISP) for homogeneous background medium is investigated numerically using the transmission-line matrix (TLM) method. By transforming all electromagnetic sources and fields into their equivalent link impulses within a TLM computational domain, a discrete linear inversion formulation is developed. Our formulation solves for the unknown source distribution inside a closed region using the knowledge of the near-field data on its boundary. Unlike the conventional frequency-domain treatments, both our source solution and the field measurements are in the time domain. The nonuniqueness of the ISP is addressed by additionally imposing smoothness constraints that minimize the first-order time and spatial derivatives of the source distribution. Our algorithm is illustrated through a number of numerical examples. It is also shown that our algorithm is robust against the noisy field measurements.