In this work, a TDSIE solver is proposed for analyzing transient plasmonic interactions. The proposed solver utilizes the well-known Poggio-Miller-Chan-Harrington-Wu-Tsai (PMCHWT) SIE formalism (L. N. Medgyesi-Mitschang et al., J.Opt.Soc.Am.A, 11(4), 1383-1398, 1994) to describe the scattered fields in terms of equivalent surface electric and magnetic currents introduced at material interfaces and the time domain Green function of the plasmonic medium (H. Wilhelmsson et al., Physica Scripta., 52, 102-107, 1995). Equivalent currents are expanded in terms of Rao-Wilton-Glisson
(RWG) (S. M. Rao et al., IEEE Trans. Antennas Propagat., 30(3), 409-418, 1982) functions in space and polynomial interpolants (D.G. Manara et al., IEEE Trans. Antennas Propagat., 45(3), 527-532, 1997) in time. Inserting these expansions into the TDSIE and Galerkin testing the resulting equation at time samples results in a matrix system of equations. This matrix system is solved for current expansion coefficients using the marching-on-in-time (MOT) technique.